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Homework

Unit 1 · Lesson 6: Estimate Irrational Numbers

Example # 1

Directions: Determine if the expression is a perfect square. If not, determine the two perfect squares that the square root lies between

√ 4

Solution:

When creating a perfect square with an area of 4, the length needs to be 2 and the width needs to be 2.

A square is a plane figure with four equal sides and angles. To prove that 4 is a perfect square, build a square that has an
area of 4.

The integer multiplied by itself to have a product of four is 2.

• (^) √ 4 is the same as (^) √ 2 ⋅ 2. This indicates that the square root of 4 is 2.

22 = 2⋅2 = 4, therefore

√ 4 =√ 2 ⋅ 2 = 2

Example # 2

√ 20

Solution:

20 is not a perfect square and this can be proved since a square cannot be built with an area of 20

Since √ 20 is not a perfect square, find what two perfect squares it lies in between.

20 lies between 16 and 25, which are both perfect squares.

Since √ 16 = 4 and √ 25 = 5, √ 20 must lie between 4 and 5.

Answer: Since √ 20 is not a perfect square, and √ 20 lies between 4 and 5.

4

5

1 0 1 2 3 4 5 6 7 8 9 10 11 12
roots

squares 16 20 25

Homework