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.

easy dubs we gettin out of the gulag with this one

You are quite the absurd person and I honestly love it

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

wow i never actually thought i would ever understand square roots. but theyre actually kinda easy. (i say that now, of course)

lmao i'm sure it'll get harder for us

my math test is tmr pls pray for me

same, I have two. let's hope we both survive...

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

Main content

Square roots of perfect squares

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...”
(68 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
  (14 votes)
ELLEN
Posted 5 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...”
(38 votes)
Answer
- thomas tomiwa
  Posted 5 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...”
  (32 votes)
nimitthnithin
Posted 2 months ago. Direct link to nimitthnithin's post “easy dubs we gettin out o...”
easy dubs we gettin out of the gulag with this one
Button navigates to signup pageComment on nimitthnithin's post “easy dubs we gettin out o...”
(46 votes)
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- Anjali Bliss
  Posted 2 months ago. Direct link to Anjali Bliss's post “You are quite the absurd ...”
  You are quite the absurd person and I honestly love it
  Button navigates to signup page
  (17 votes)
kumaa881
Posted a month ago. Direct link to kumaa881's post “the most fun part of khan...”
the most fun part of khan academy is definitely reading the comments...
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(42 votes)
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- hblowder
  Posted a month ago. Direct link to hblowder's post “lol i agree”
  lol i agree
  Comment on hblowder's post “lol i agree”
  (9 votes)
Saaketh Gaddam
Posted 5 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 5 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 ...”
  (24 votes)
nathias.grant
Posted a month ago. Direct link to nathias.grant's post “we getting outta the hood...”
we getting outta the hood with this now finna get to college after this
Button navigates to signup pageComment on nathias.grant's post “we getting outta the hood...”
(24 votes)
Answer
minnieli1223
Posted 6 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 ...”
(12 votes)
Answer
- Shawn
  Posted 6 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
  (4 votes)
Cami
Posted a month ago. Direct link to Cami's post “my math test is tmr pls p...”
my math test is tmr pls pray for me
Button navigates to signup pageComment on Cami's post “my math test is tmr pls p...”
(13 votes)
Answer
- CuriousFox14
  Posted a month ago. Direct link to CuriousFox14's post “same, I have two. let's h...”
  same, I have two. let's hope we both survive...
  Comment on CuriousFox14's post “same, I have two. let's h...”
  (9 votes)
Mikaela Matrille
Posted a month ago. Direct link to Mikaela Matrille's post “wow i never actually thou...”
wow
i never actually thought i would ever understand square roots. but theyre actually kinda easy. (i say that now, of course)
Button navigates to signup pageComment on Mikaela Matrille's post “wow i never actually thou...”
(14 votes)
Answer
- Envxsion
  Posted a month ago. Direct link to Envxsion's post “lmao i'm sure it'll get h...”
  lmao i'm sure it'll get harder for us
  Comment on Envxsion's post “lmao i'm sure it'll get h...”
  (2 votes)
maruandtotoro
Posted 7 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 7 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)

8th grade

Course: 8th grade > Unit 1