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## 8th grade (Illustrative Mathematics)

### Unit 8: Lesson 4

Lesson 5: Reasoning about square roots# Approximating square roots walk through

CCSS.Math:

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:**

### Reflection question

## Practice Set 1:

## 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:

**Step 2:**Order the numbers from least to greatest:

**The answer**:

### Reflection question

## Practice Problem 2:

## Example

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

**Step 1:**Create a table of perfect squares.

**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?"

**The answer:**

## Practice Problem 3:

## Want to join the conversation?

- Is this the easiest way of doing this?(27 votes)
- 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.(12 votes) - how do I estimate the square root of 78?(6 votes)
- 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(10 votes)

- 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?(6 votes)
- If you do, then the answer would still be the same, so yes you can!(2 votes)

- 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(5 votes)
- you need it in life when you're a rocket scientist!(2 votes)

- and what is the answer? not the solution, i want what is the answer , and how did it get it(5 votes)
- Think you everyone for helping me to learn.(3 votes)
- why are we still here?(2 votes)
- I don't understand this math(3 votes)