how do I estimate the square root of 78?

So, 8 squared equals 64 and 9 squared equals 81. It will be in between those two numbers. But which one is 78 closer to? 81. So, the square root of 78 will be closer to 9. 8.8 to be more accurate ;P

On the problem where we need to order the numbers 5 squared, 4 squared, and the square root of 14, it says 5, 4, and square root of 14. Can you change it so that it says 5 squared and 4 squared?

If you do, then the answer would still be the same, so yes you can!

I loved the video very helpful thanks! I was totally overthinking it. Not sure when I would need this in life, but cool to know I guess. haha

you need it in life when you're a rocket scientist!

Main content

8th grade

Course: 8th grade > Unit 1

Lesson 4: Approximating irrational numbers

Approximating square roots walk through

Google Classroom

Walk through a series of questions and examples that will help you learn how to approximate square roots.

In this article, you'll learn how to approximate square roots! Let's dive in.

Example

Spot the pattern:

left parenthesis, square root of, start color #e07d10, 25, end color #e07d10, end square root, right parenthesis, squared, equals, start color #e07d10, 25, end color #e07d10

left parenthesis, square root of, start color #e07d10, 6, end color #e07d10, end square root, right parenthesis, squared, equals, start color #e07d10, 6, end color #e07d10

left parenthesis, square root of, start color #e07d10, 9482, end color #e07d10, end square root, right parenthesis, squared, equals, start color #e07d10, 9482, end color #e07d10

Reflection question

When you square the square root of a number...

Practice Set 1:

Problem 1A

Current

left parenthesis, square root of, 16, end square root, right parenthesis, squared, equals
Your answer should be
an integer, like 6
a simplified proper fraction, like 3, slash, 5
a simplified improper fraction, like 7, slash, 4
a mixed number, like 1, space, 3, slash, 4
an exact decimal, like 0, point, 75
a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Example

Without using a calculator, order the following numbers from least to greatest.

square root of, 30, end square root, 5, 6

Step 1: Square each of the numbers:

n, colon square root of, 30, end square root 5 6
n, squared, colon start color #11accd, 30, end color #11accd start color #1fab54, 25, end color #1fab54 start color #ca337c, 36, end color #ca337c

n, colon	square root of, 30, end square root	5	6
n, squared, colon	start color #11accd, 30, end color #11accd	start color #1fab54, 25, end color #1fab54	start color #ca337c, 36, end color #ca337c

Step 2: Order the numbers from least to greatest:

n, colon 5 square root of, 30, end square root 6
n, squared, colon start color #1fab54, 25, end color #1fab54 start color #11accd, 30, end color #11accd start color #ca337c, 36, end color #ca337c

n, colon	5	square root of, 30, end square root	6
n, squared, colon	start color #1fab54, 25, end color #1fab54	start color #11accd, 30, end color #11accd	start color #ca337c, 36, end color #ca337c

The answer:

5 square root of, 30, end square root 6


5	square root of, 30, end square root	6

Reflection question

When ordering square roots and integers, which of the following is the best strategy?

For example: 6, comma, square root of, 28, end square root, comma, 5.

(Choice A)
Square just the square roots. For example: 6, comma, left parenthesis, square root of, 28, end square root, right parenthesis, start superscript, start color #e84d39, 2, end color #e84d39, end superscript, comma, 5.
(Choice B)
Square both the square roots and the integers. For example: 6, start superscript, start color #e84d39, 2, end color #e84d39, end superscript, comma, left parenthesis, square root of, 28, end square root, right parenthesis, start superscript, start color #e84d39, 2, end color #e84d39, end superscript, comma, 5, start superscript, start color #e84d39, 2, end color #e84d39, end superscript.

Practice Problem 2:

Without using a calculator, order the following numbers from least to greatest.

Example

Without using a calculator, find two consecutive integers to complete the following inequality.

question mark, is less than, square root of, 97, end square root, is less than, question mark

Step 1: Create a table of perfect squares.

n, colon 7 8 9 10 11
n, squared, colon 49 64 81 100 121

n, colon	7	8	9	10	11
n, squared, colon	49	64	81	100	121

Step 2: Ask yourself, "Where does n, equals, square root of, start color #1fab54, 97, end color #1fab54, end square root fit into the table?"

n, colon 7 8 start color #ca337c, 9, end color #ca337c square root of, start color #1fab54, 97, end color #1fab54, end square root start color #11accd, 10, end color #11accd 11
n, squared, colon 49 64 81 start color #1fab54, 97, end color #1fab54 100 121

n, colon	7	8	start color #ca337c, 9, end color #ca337c	square root of, start color #1fab54, 97, end color #1fab54, end square root	start color #11accd, 10, end color #11accd	11
n, squared, colon	49	64	81	start color #1fab54, 97, end color #1fab54	100	121

The answer:

start color #ca337c, 9, end color #ca337c, is less than, square root of, start color #1fab54, 97, end color #1fab54, end square root, is less than, start color #11accd, 10, end color #11accd

Practice Problem 3:

Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.

is less than, square root of, 56, end square root, is less than

Want to join the conversation?

Sort by:

Shaurya_Patel
Posted 6 years ago. Direct link to Shaurya_Patel's post “Is this the easiest way o...”
Is this the easiest way of doing this?
Button navigates to signup pageComment on Shaurya_Patel's post “Is this the easiest way o...”
(34 votes)
Answer
- Coolman
  Posted 5 months ago. Direct link to Coolman's post “yes it is”
  yes it is
  Comment on Coolman's post “yes it is”
  (8 votes)
WalterF
Posted a month ago. Direct link to WalterF's post “⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉...”
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀
⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
Button navigates to signup pageComment on WalterF's post “⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉...”
(22 votes)
Answer
- liam pederson
  Posted 19 days ago. Direct link to liam pederson's post “love it”
  love it
  Button navigates to signup page
  (1 vote)
1203197
Posted 5 years ago. Direct link to 1203197's post “Does it make sense if I f...”
Does it make sense if I for example have the equation-14.5 (looking for the squared root). And i see what perfect square is less than 14 and what perf square is greater than 14 than order them like you do from least to greater. I than take those 2 other numbers and combine there squared roots.EX)
1- 3*=9 ?*=14 4*=16
2- 3.9* approximately =‘s. 14.5
3- I used * as squared and my answer might not be exact but in estimation it’s not always perfect.
Button navigates to signup pageButton navigates to signup page
(13 votes)
Answer
- gordonmalik2020
  Posted 2 months ago. Direct link to gordonmalik2020's post “yes it is”
  yes it is
  Button navigates to signup page
  (0 votes)
Aidan
Posted 6 years ago. Direct link to Aidan's post “how do I estimate the squ...”
how do I estimate the square root of 78?
Button navigates to signup pageComment on Aidan's post “how do I estimate the squ...”
(6 votes)
Answer
- Isabelle Hammonds
  Posted 3 years ago. Direct link to Isabelle Hammonds's post “So, 8 squared equals 64 a...”
  So, 8 squared equals 64 and 9 squared equals 81. It will be in between those two numbers. But which one is 78 closer to? 81. So, the square root of 78 will be closer to 9. 8.8 to be more accurate ;P
  Comment on Isabelle Hammonds's post “So, 8 squared equals 64 a...”
  (13 votes)
aaron.623713
Posted 4 months ago. Direct link to aaron.623713's post “why are we still here?”
why are we still here?
Button navigates to signup pageComment on aaron.623713's post “why are we still here?”
(6 votes)
Answer
- FrostAxol101
  Posted 3 months ago. Direct link to FrostAxol101's post “To Suffer my friend”
  To Suffer my friend
  Comment on FrostAxol101's post “To Suffer my friend”
  (5 votes)
Daniel Garcia
Posted 7 years ago. Direct link to Daniel Garcia's post “On the problem where we n...”
On the problem where we need to order the numbers 5 squared, 4 squared, and the square root of 14, it says 5, 4, and square root of 14. Can you change it so that it says 5 squared and 4 squared?
Button navigates to signup pageComment on Daniel Garcia's post “On the problem where we n...”
(6 votes)
Answer
- Marcimus when the imposter is susඞඞ
  Posted 8 months ago. Direct link to Marcimus when the imposter is susඞඞ's post “If you do, then the answe...”
  If you do, then the answer would still be the same, so yes you can!
  Button navigates to signup page
  (2 votes)
Allison Jolene Essex
Posted 3 years ago. Direct link to Allison Jolene Essex's post “I loved the video very he...”
I loved the video very helpful thanks! I was totally overthinking it. Not sure when I would need this in life, but cool to know I guess. haha
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Logan
  Posted 4 months ago. Direct link to Logan's post “you need it in life when ...”
  you need it in life when you're a rocket scientist!
  Comment on Logan's post “you need it in life when ...”
  (3 votes)
kennedyarmstrong
Posted 6 months ago. Direct link to kennedyarmstrong's post “do i have to?”
do i have to?
Button navigates to signup pageComment on kennedyarmstrong's post “do i have to?”
(3 votes)
Answer
anthony.shockley
Posted a month ago. Direct link to anthony.shockley's post “help the school is holdin...”
help the school is holding us hostage (I just don't wanna be here😁)
Button navigates to signup pageComment on anthony.shockley's post “help the school is holdin...”
(3 votes)
Answer
Darrelle $$ man
Posted 5 years ago. Direct link to Darrelle $$ man's post “Think you everyone for he...”
Think you everyone for helping me to learn.
Button navigates to signup pageComment on Darrelle $$ man's post “Think you everyone for he...”
(3 votes)
Answer
- agmercer
  Posted a month ago. Direct link to agmercer's post “you're welcome <333 <3 <3”
  you're welcome <333 <3 <3
  Button navigates to signup page
  (1 vote)