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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