ROOTS AND REAL NUMBERS WORKSHEET

Problems 1 to 5 : Find each root.

Problem 1 : 

√36

Problem 2 : 

-√49

Problem 3 : 

³√-64

Problem 4 : 

√(1/9)

Problem 5 : 

√(16/25)

Problem 6 : 

Lily wants to plant a square garden of wildflowers. She has enough wildflower seeds to cover 19 square ft. Estimate to the nearest tenth the side length of a square with an area of 19 square ft.

Problems 7 to 10 : Write all classifications that apply to each real number.

Problem 7 : 

8/9

Problem 8 : 

15

Problem 9 : 

√26

Problem 10 : 

√100

Detailed Answer Key

Problems 1 to 5 : Find each root.

Problem 1 : 

√36

Solution : 

=  √36

Think : What number squared equals 36?

=  √6²

=  6

Problem 2 : 

-√49

Solution : 

=  -√49

Think : What number squared equals 49?

=  -√7²

=  -7

Problem 3 : 

³√-64

Solution : 

=  ³√-64

Think : What number cubed equals -125?

[(-4)(-4)(-4)  =  16(-4)  =  -64]

=  ³√(-4)³

=  -4

Problem 4 : 

√(1/9)

Solution : 

=  √(1/9)

Think : What number squared equals 1/9?

=  √(1/3)²

=  1/3

Problem 5 : 

√(16/25)

Solution : 

=  √(16/25)

Think : What number squared equals 16/25?

=  √(4/5)²

=  4/5

Problem 6 : 

Lily wants to plant a square garden of wildflowers. She has enough wildflower seeds to cover 19 square ft. Estimate to the nearest tenth the side length of a square with an area of 19 square ft.

Solution : 

Because the area of the square is 19 square ft, then each side of the square is √19 ft.

19 is not a perfect square, so find the two consecutive perfect squares that 19 is between : 16 and 25.

√19 is between √16 and √25, or 4 and 5.

Refine the estimate.

4.3 :  4.3²  =  18.49  too low √19 is greater than 4.3

4.4 :  4.4²  =  19.36  too high √19 is less than 4.4

4.35 :  4.35²  =  18.9225  too low √19 is greater than 4.35

Because 4.35 is too low and 4.4 is too high, √19 is between 4.35 and 4.4.

Rounded to the nearest tenth,

√19  ≈  4.4

The side length of the plot is about 4.4 ft.

Problems 7 to 10 : Write all classifications that apply to each real number.

Problem 7 : 

8/9

Solution : 

8/9 is in the form a/b, where a and b are integers (b ≠ 0).

8 ÷ 9  =  0.8888…

8/9 can be written as a repeating decimal.

So, the classification of 8/9 is rational, repeating decimal.

Problem 8 : 

15

Solution : 

15 can be written in the form a/b.

15  =  15/1

15 can be written as a terminating decimal.

15  =  15.0

So, the classification of 15 is rational, terminating decimal, integer, whole, natural. 

Problem 9 : 

√26

Solution : 

26 is not a perfect square, so √26 is irrational.

Problem 10 : 

√100

Solution : 

100 is a perfect square, so √100 is irrational.

√100  =  √10²  =  10

10 can be written in the form a/b.

10  =  10/1

10 can be written as a terminating decimal.

10  =  10.0

So, the classification of √100 is rational, terminating decimal, integer, whole, natural. 

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