Can an exponent be a negative number?

You already know that an exponent represents the number of times you have to multiply a number by itself. A negative exponent is equivalent to the inverse of the same number with a positive exponent. There is nothing special about solving a problem that includes negative exponentials.

is this 8th-grade math? im in 5th grade:+

That is awesome for you continue to learn ahead

What happens if try to find the the square root of an imperfect square

Most probably it will be an irrational number in which case we can only approximate its value. However, sometimes we can write the radicand as a fraction of two perfect squares. Example: √5.76 = √(576∕100) = √(144∕25) = √(12²∕5²) = 12∕5 = 2.4

I just noticed something really interesting (I think): If I can't remember a square of some numbers (7^2 and 8^2 can be a bit tricky for me for some reason) but I remember the square number of the root that comes before it (6 and 36 in the case I'm trying to find 7^2), I can do 36+6 to make it into 6*7, and then add a 7 to make it into a 7*7. I tried to play around and find a rule and I think I found the formula: n^2 + 2n + 1 = ( n + 1 )^2 (where n is the root number of the square that you do know). if you would visualize the numbers on a grid, the n^2 is the area of the square, while the 2n+1 is the number of the additional units the is added on the side. It's easier to see it on a times table: When looking at 25, the number diagonally next to it is 36. If you count the 'units' (the other multiplies that are on the same axes that leads toward 36 IE: 3,6,9 up to 36 on both sides) they will be the same as the 2n+1. I tried to find a formula for a square of a root that isn't immediately follows the root I know. example: 3^2 = 9, 5^2 = ?. unfortunately I couldn't think on one consistent formula, because there is always a need to add more and (n+1) with more additional 1s the further the number is. does the formula I found have a name? I'm pretty sure I wasn't the first to think of that lol

You can use the pascal's triangle I suppose Edit1: here: https://en.wikipedia.org/wiki/Polynomial_expansion Edit2: Sorry that is not true. That applies to expansions with higher powers, but not between different sqaures. But maybe you can look at sum of squares where ∑x^2 = n(n+1)(2n+1)/6

So, a perfect square is basically the answer to an exponent? (ex. 2^2(4), 12^12(144))

it is an integer with a square root that is also an integer

How can we use square roots in life?

There are many ways in life you can use square roots. Some of them include a mathmatician, engineer, architect, carpenter, etc.

can a decimal have a square root

Yes, decimals can have square roots. For example, the (principal) square root of 0.64 is 0.8, since 0.8*0.8 = 0.64.

How to calculate imperfect squares?

imperfect square roots (example: 32 SQUARE)(I am going to do square uppercased because I don't know how to make a square root sign) 32 SQUARE start with the number you think is closest to this number 25 SQUARE than the other closest 36 SQUARE than just find the root of these numbers 5 6 it is between 5 and 6 hope this helped and may God bless your day

Would you do the same for a negative square root ?🤔

You cannot find the negative square root of a number. Think of what square roots are. If we take 36 and find the square root, you'll see it's 6. Because 6 x 6 = 36. We multiply it by itself and it gives us 36. We can't do this with negatives. Consider -36 and finding the square root of that. Which number multiplied by itself will get -36? Well, remember the rules we have for multiplying negatives and positives. negative x negative = positive negative x positive = positive positive x positive = positive. It can't be -6, because that will give us a positive number, instead of -36. It can't be 6, because that will also give us a positive number instead of -36. So, negatives can't have square roots. You'll learn in more advanced classes what we do in these cases.

Main content

Square roots of perfect squares

CCSS.Math:

8.EE.A.2

Google Classroom

Learn how to find the square root of perfect squares like 25, 36, and 81.

Let's start by taking a look at an example evaluating the square root of start color #1fab54, 25, end color #1fab54:

square root of, start color #1fab54, 25, end color #1fab54, end square root, equals, question mark

Step 1: Ask, "What number squared equals start color #1fab54, 25, end color #1fab54?"

Step 2: Notice that start color #11accd, 5, end color #11accd squared equals start color #1fab54, 25, end color #1fab54.

start color #11accd, 5, end color #11accd, squared, equals, start color #11accd, 5, end color #11accd, times, start color #11accd, 5, end color #11accd, equals, start color #1fab54, 25, end color #1fab54

The answer

square root of, start color #1fab54, 25, end color #1fab54, end square root, equals, start color #11accd, 5, end color #11accd

Here's a question to make sure you understood:

How can we be sure that start color #11accd, 5, end color #11accd is the right answer?

(Choice A)
Because start color #11accd, 5, end color #11accd is half of 10.
(Choice B)
Because start color #11accd, 5, end color #11accd is an odd number.
(Choice C)
Because start color #11accd, 5, end color #11accd times itself equals 25.

Connection to a square

Finding the square root of start color #1fab54, 25, end color #1fab54 is the same as finding the side length of a square with an area of start color #1fab54, 25, end color #1fab54.

A square with an area of start color #1fab54, 25, end color #1fab54 has a side length of start color #11accd, 5, end color #11accd.

Practice Set 1:

Problem 1A

Current

4, squared, equals

Reflection question

Which claim shows how square roots work?

(Choice A)
Claim 1: space, space, space, 7, squared, equals, 49 and square root of, 49, end square root, equals, 7
(Choice B)
Claim 2: space, space, space, 7, squared, equals, square root of, 7, end square root

Practice Set 2:

Problem 2A

Current

square root of, 1, end square root, equals

Practice Set 3:

Problem 3A

Current

square root of, 121, end square root, equals

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cyanne.13.edwards
Posted 7 years ago. Direct link to cyanne.13.edwards's post “Can an exponent be a nega...”
Can an exponent be a negative number?
Button navigates to signup pageComment on cyanne.13.edwards's post “Can an exponent be a nega...”
(62 votes)
Answer
- Joann
  Posted 3 years ago. Direct link to Joann's post “You already know that an ...”
  You already know that an exponent represents the number of times you have to multiply a number by itself. A negative exponent is equivalent to the inverse of the same number with a positive exponent. There is nothing special about solving a problem that includes negative exponentials.
  Button navigates to signup page
  (9 votes)
ELLEN
Posted 4 years ago. Direct link to ELLEN's post “is this 8th-grade math? i...”
is this 8th-grade math?
im in 5th grade:+
Button navigates to signup pageComment on ELLEN's post “is this 8th-grade math? i...”
(34 votes)
Answer
- thomas tomiwa
  Posted 4 years ago. Direct link to thomas tomiwa's post “That is awesome for you c...”
  That is awesome for you continue to learn ahead
  Comment on thomas tomiwa's post “That is awesome for you c...”
  (28 votes)
Saaketh Gaddam
Posted 4 years ago. Direct link to Saaketh Gaddam's post “What happens if try to fi...”
What happens if try to find the
the square root of an imperfect square
Button navigates to signup pageComment on Saaketh Gaddam's post “What happens if try to fi...”
(16 votes)
Answer
- Jerry Nilsson
  Posted 4 years ago. Direct link to Jerry Nilsson's post “Most probably it will be ...”
  Most probably it will be an irrational number in which case we can only approximate its value.
  
  However, sometimes we can write the radicand as a fraction of two perfect squares.
  Example: √5.76 = √(576∕100) = √(144∕25) = √(12²∕5²) = 12∕5 = 2.4
  Comment on Jerry Nilsson's post “Most probably it will be ...”
  (22 votes)
minnieli1223
Posted 5 years ago. Direct link to minnieli1223's post “I just noticed something ...”
I just noticed something really interesting (I think):

If I can't remember a square of some numbers (7^2 and 8^2 can be a bit tricky for me for some reason) but I remember the square number of the root that comes before it (6 and 36 in the case I'm trying to find 7^2),
I can do 36+6 to make it into 6*7, and then add a 7 to make it into a 7*7.

I tried to play around and find a rule and I think I found the formula:
n^2 + 2n + 1 = ( n + 1 )^2
(where n is the root number of the square that you do know).

if you would visualize the numbers on a grid, the n^2 is the area of the square, while the 2n+1 is the number of the additional units the is added on the side.

It's easier to see it on a times table: When looking at 25, the number diagonally next to it is 36. If you count the 'units' (the other multiplies that are on the same axes that leads toward 36 IE: 3,6,9 up to 36 on both sides) they will be the same as the 2n+1.

I tried to find a formula for a square of a root that isn't immediately follows the root I know. example: 3^2 = 9, 5^2 = ?.
unfortunately I couldn't think on one consistent formula, because there is always a need to add more and (n+1) with more additional 1s the further the number is.

does the formula I found have a name? I'm pretty sure I wasn't the first to think of that lol
Button navigates to signup pageComment on minnieli1223's post “I just noticed something ...”
(11 votes)
Answer
- Shawn
  Posted 5 years ago. Direct link to Shawn's post “You can use the pascal's ...”
  You can use the pascal's triangle I suppose
  
  Edit1: here: https://en.wikipedia.org/wiki/Polynomial_expansion
  
  Edit2: Sorry that is not true. That applies to expansions with higher powers, but not between different sqaures.
  But maybe you can look at sum of squares where
  ∑x^2 = n(n+1)(2n+1)/6
  Button navigates to signup page
  (3 votes)
maruandtotoro
Posted 6 years ago. Direct link to maruandtotoro's post “So, a perfect square is b...”
So, a perfect square is basically the answer to an exponent? (ex. 2^2(4), 12^12(144))
Button navigates to signup pageComment on maruandtotoro's post “So, a perfect square is b...”
(10 votes)
Answer
- suzannac
  Posted 6 years ago. Direct link to suzannac's post “it is an integer with a s...”
  it is an integer with a square root that is also an integer
  Comment on suzannac's post “it is an integer with a s...”
  (10 votes)
aniza white
Posted 2 years ago. Direct link to aniza white's post “How can we use square roo...”
How can we use square roots in life?
Button navigates to signup pageComment on aniza white's post “How can we use square roo...”
(8 votes)
Answer
- ⭐BEST20042007⭐
  Posted 2 years ago. Direct link to ⭐BEST20042007⭐'s post “There are many ways in li...”
  There are many ways in life you can use square roots. Some of them include a mathmatician, engineer, architect, carpenter, etc.
  Comment on ⭐BEST20042007⭐'s post “There are many ways in li...”
  (5 votes)
jl974294
Posted 6 years ago. Direct link to jl974294's post “How do you solve square r...”
How do you solve square roots that can't be squared easily?
Button navigates to signup pageComment on jl974294's post “How do you solve square r...”
(8 votes)
Answer
- Catalina Mangiafico
  Posted 3 years ago. Direct link to Catalina Mangiafico's post “what i do is if the numbe...”
  what i do is if the number is less then 81 then I go through all of the numbers 1-9 to see if they match up. if its greater than 144 then i just use a calculator
  Comment on Catalina Mangiafico's post “what i do is if the numbe...”
  (0 votes)
osagier430
Posted 3 years ago. Direct link to osagier430's post “can a decimal have a squa...”
can a decimal have a square root
Button navigates to signup pageComment on osagier430's post “can a decimal have a squa...”
(6 votes)
Answer
- Ian Pulizzotto
  Posted 3 years ago. Direct link to Ian Pulizzotto's post “Yes, decimals can have sq...”
  Yes, decimals can have square roots. For example, the (principal) square root of 0.64 is 0.8, since 0.8*0.8 = 0.64.
  Comment on Ian Pulizzotto's post “Yes, decimals can have sq...”
  (4 votes)
FoxLegend
Posted 6 years ago. Direct link to FoxLegend's post “How to calculate imperfec...”
How to calculate imperfect squares?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Autumn
  Posted 6 years ago. Direct link to Autumn's post “imperfect square roots (e...”
  imperfect square roots (example: 32 SQUARE)(I am going to do square uppercased because I don't know how to make a square root sign)
  32 SQUARE
  start with the number you think is closest to this number
  25 SQUARE
  than the other closest
  36 SQUARE
  than just find the root of these numbers
  5
  6
  it is between 5 and 6
  hope this helped and may God bless your day
  Comment on Autumn's post “imperfect square roots (e...”
  (8 votes)
Gigi💙
Posted 6 years ago. Direct link to Gigi💙's post “Would you do the same for...”
Would you do the same for a negative square root ?🤔
Button navigates to signup pageComment on Gigi💙's post “Would you do the same for...”
(3 votes)
Answer
- Benny C
  Posted 6 years ago. Direct link to Benny C's post “You cannot find the negat...”
  You cannot find the negative square root of a number. Think of what square roots are. If we take 36 and find the square root, you'll see it's 6. Because 6 x 6 = 36. We multiply it by itself and it gives us 36.
  
  We can't do this with negatives. Consider -36 and finding the square root of that. Which number multiplied by itself will get -36?
  
  Well, remember the rules we have for multiplying negatives and positives.
  negative x negative = positive
  negative x positive = positive
  positive x positive = positive.
  
  It can't be -6, because that will give us a positive number, instead of -36.
  It can't be 6, because that will also give us a positive number instead of -36.
  
  So, negatives can't have square roots.
  
  You'll learn in more advanced classes what we do in these cases.
  Comment on Benny C's post “You cannot find the negat...”
  (9 votes)

8th grade

Course: 8th grade > Unit 1