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### Course: Grade 8 (VA SOL) > Unit 6

Lesson 3: Approximating irrational numbers- Approximating square roots
- Approximating square roots walk through
- Approximating square roots
- Comparing irrational numbers with radicals
- Comparing irrational numbers
- Approximating square roots to hundredths
- Comparing values with calculator
- Comparing irrational numbers with a calculator

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# 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:**

### Reflection question

## Practice Set 1:

## Example

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

, $\sqrt{30}$ , $5$ $6$

**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

**The answer:**

## Practice Problem 3:

## Want to join the conversation?

- Is this the easiest way of doing this?(52 votes)
- how do I estimate the square root of 78?(7 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(23 votes)

- This is waaaaaay too easy!(12 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.(13 votes) - There isn't a square button on your calculator can you add it please(9 votes)
- Just multiply the number by itself. :/

(e.g. 6^2 = 6x6.)(9 votes)

- Dunno, That's Just Life, They Just
**HAD**To Make Math Hard.(4 votes)

- Confusing, but I think I'll get the hang of it(8 votes)
- is they a way to solve it easily(6 votes)
- I think that if you want to see the easiest way. It's to find the square root of it; (ex 155). And find its perfect square root and find the closest whole number below and above it(4 votes)

- is there a simpler way to do this(5 votes)
- Yeah, if there is a root and you square it, then the square and the root cancel out.

As for finding the consecutive integers, use the process of elimination. and square(6 votes)