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### Unit 8: Lesson 4

Lesson 5: Reasoning about square roots

# Approximating square roots walk through

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...

Problem 1A

## 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, colonsquare root of, 30, end square root56
n, squared, colonstart color #11accd, 30, end color #11accdstart color #1fab54, 25, end color #1fab54start color #ca337c, 36, end color #ca337c
Step 2: Order the numbers from least to greatest:
n, colon5square root of, 30, end square root6
n, squared, colonstart color #1fab54, 25, end color #1fab54start color #11accd, 30, end color #11accdstart color #ca337c, 36, end color #ca337c
5square root of, 30, end square root6

### 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.

## 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, colon7891011
n, squared, colon496481100121
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, colon78start color #ca337c, 9, end color #ca337csquare root of, start color #1fab54, 97, end color #1fab54, end square rootstart color #11accd, 10, end color #11accd11
n, squared, colon496481start color #1fab54, 97, end color #1fab54100121
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?

• Is this the easiest way of doing this?
• yes it is
• 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.
• 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!