approximate non-perfect squares

Approximate values for non-perfect squares

learn how to use perfect squares to approximate non-perfect squares to the nearest tenth.

in this lesson, we will...

learn how to and practice approximating non-perfect squares

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What does "Approximate" mean?

to come close to the actual, but not exact or completely accurate.

*it is very similar to estimating.

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​Non-Perfect square

a perfect square is the product of a rational number multiplied by itself.

For example:

5² = 25 so √25 is 5

*they are "nice, neat" whole numbers*

Perfect squares are RATIONAL NUMBERS

​Perfect Square

But first, let's review

a non-perfect square is an integer whose square is not a whole number.

For example:

√7 = 2.645751....

*goes on forever without repeating*

Non-perfect squares are IRRATIONAL NUMBERS

Match

Match the following

• perfect squares are...

• non-perfect squares are...

• rational numbers are...

• irrational numbers are...

rational numbers

irrational numbers

able to be written as fractions

not able to be written as fractions

• rational numbers

• irrational numbers

• able to be written as fractions

• not able to be written as fractions

Multiple Choice

Natural numbers (counting numbers) are...

• rational

• irrational

Multiple Choice

whole numbers (zero and up) are...

• rational

• irrational

Multiple Choice

$$\pi$$ pi is...

• rational

• irrational

Multiple Choice

integers (positive and negative whole numbers) are...

• rational

• irrational

Multiple Choice

non-perfect squares are...

• rational

• irrational

Multiple Choice

repeating decimals are...

• rational

• irrational

Multiple Choice

perfect squares are..

• rational

• irrational

Multiple Choice

fractions with integers are..

• rational

• irrational

Multiple Choice

non-repeating and non-terminating (goes on forever without repeating) decimals are...

• rational

• irrational

Multiple Choice

terminating decimals (have an end) are...

• rational

• irrational

Multiple Select

select all the perfect squares

• $$\sqrt[]{81}$$

• $$\sqrt[]{27}$$

• $$\sqrt[]{64}$$

• $$\sqrt[]{121}$$

• $$\sqrt[]{65}$$

Reminder: in this lesson, we will...

learn how to and practice approximating non-perfect squares

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How do you approximate non-perfect Squares?

In order to approximate a non-perfect square, you use perfect squares to get close to the true answer.

the next slide has a video that shows some examples of doing this.

*keep in mind, that we will not be using calculators.

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Reorder

order the following from LEAST to GREATEST (small --> big)

• 2.234

• 2.24

• 2.455

• 2.545

• 2.688

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Let's take it step by step

we are going to go through some of the steps to practice approximating non-perfect squares

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Multiple Select

Pick 2 perfect squares you could use to approximate the $$\sqrt[]{10}$$

• $$\sqrt[]{9}$$

• $$\sqrt[]{11}$$

• $$\sqrt[]{16}$$

• $$\sqrt[]{12}$$

• $$\sqrt[]{25}$$

Why would we use √9 and √16 ?

They are perfect squares which means their answers are whole numbers

the √9 = 3 and √16 = 4

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Multiple Choice

The $$\sqrt[]{10}$$ is likely going to be closer to...

• $$\sqrt[]{9}$$

• $$\sqrt[]{16}$$

How do you know √9 is closer to √10 ?

9 is closer to 10 than it is to 16.

this means that the answer is going to be closer to 3 than it is to 4.

*remember your answer is going to be a decimal

Multiple Select

What would you approximate the $$\sqrt[]{10}$$ is rounded to the nearest tenth?

• 3.1

• 3.2

• 3.4

• 3.5

the true answer for √10 is...

3.1622776602...

Multiple Select

Pick 2 perfect squares you could use to approximate the $$\sqrt[]{43}$$

• $$\sqrt[]{30}$$

• $$\sqrt[]{40}$$

• $$\sqrt[]{49}$$

• $$\sqrt[]{36}$$

• $$\sqrt[]{25}$$

Why would we use √36 and √49 ?

They are perfect squares which means their answers are whole numbers

the √36 = 6 and √49 = 7

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Multiple Choice

The $$\sqrt[]{43}$$ is likely going to be closer to...

• $$\sqrt[]{49}$$

• $$\sqrt[]{36}$$

How do you know √49 is closer to √43 ?

49 is closer to 43 than it is to 36.

this means that the answer is going to be closer to 7 than it is to 6.

*remember your answer is going to be a decimal

Multiple Select

What would you approximate the $$\sqrt[]{43}$$ is rounded to the nearest tenth?

• 6.4

• 6.5

• 6.6

• 6.7

• 6.8

the true answer for √43 is...

6.5574385243...

Assignment:

do Parts 2 and the top half of Part 3 of the "Unit 5 Assignment Pack" on OneNote.

Subject | Subject

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