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### Course: Grade 8 math (FL B.E.S.T.)>Unit 2

Lesson 4: Approximating irrational numbers

# 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:
$\left(\sqrt{25}{\right)}^{2}=25$
$\left(\sqrt{6}{\right)}^{2}=6$
$\left(\sqrt{9482}{\right)}^{2}=9482$

### 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.
$\sqrt{30}$, $5$, $6$
Step 1: Square each of the numbers:
$n\phantom{\rule{0.222em}{0ex}}\phantom{\rule{0.222em}{0ex}}:$$\sqrt{30}$$5$$6$
${n}^{2}:$$30$$25$$36$
Step 2: Order the numbers from least to greatest:
$n\phantom{\rule{0.222em}{0ex}}\phantom{\rule{0.222em}{0ex}}:$$5$$\sqrt{30}$$6$
${n}^{2}:$$25$$30$$36$
$5$$\sqrt{30}$$6$

### Reflection question

When ordering square roots and integers, which of the following is the best strategy?
For example: $6,\sqrt{28},5$.

## 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.
$?\phantom{\rule{0.167em}{0ex}}<\sqrt{97}<\phantom{\rule{0.167em}{0ex}}?$
Step 1: Create a table of perfect squares.
$n\phantom{\rule{0.222em}{0ex}}\phantom{\rule{0.222em}{0ex}}:$$7$$8$$9$$10$$11$
${n}^{2}:$$49$$64$$81$$100$$121$
Step 2: Ask yourself, "Where does $n=\sqrt{97}$ fit into the table?"
$n\phantom{\rule{0.222em}{0ex}}\phantom{\rule{0.222em}{0ex}}:$$7$$8$$9$$\sqrt{97}$$10$$11$
${n}^{2}:$$49$$64$$81$$97$$100$$121$
$9<\sqrt{97}<10$

## Practice Problem 3:

Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
$\phantom{\rule{0.167em}{0ex}}<\sqrt{56}<\phantom{\rule{0.167em}{0ex}}$

## Want to join the conversation?

• Is this the easiest way of doing this?
• yes it is
• 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
• how r u doing
• im so bored
• This is waaaaaay too easy!
• 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.
• yes it is
• Just multiply the number by itself. :/

(e.g. 6^2 = 6x6.)
• Why is math hard