Free Printable Estimating Roots

1.

Which is the best estimate of the square root of 63?

a)

7.1

b)

7.3

c)

7.5

d)

7.9

2.

Which number has a square root that is between 7 and 8?

a)

48

b)

81

c)

60

d)

36

3.

Between which two whole numbers is the square root of 20?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

4.

Point B could represent which of the following numbers?

a)

√24

b)

√30

c)

√35

d)

√42

5.

Between which two whole numbers does the √115 fall?

a)

9 and 10

b)

10 and 11

c)

9 and 11

d)

11 and 12

6.

The area of a square is 117 square meters. Which best represents the length of a side of the square?

a)

10.8 m

b)

11 m

c)

10 m

d)

11.2 m

7.

a)

A

b)

B

c)

C

d)

D

8.

Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

9.

Which number has a square root that is between 5 and 6?

a)

48

b)

81

c)

28

d)

36

e)

20

10.

Which two integers is the square root between?

a)

7 and 8

b)

8 and 9

c)

9 and 10

d)

10 and 11

e)

6 and 7

11.

State the benchmarks you would use to approximate: $\sqrt[]{\frac{65}{190}}$

a)

$\sqrt[]{\frac{64}{196}}$

b)

$\sqrt[]{\frac{64}{190}}$

c)

$\sqrt[]{\frac{65}{196}}$

d)

$\sqrt[]{\frac{100}{200}}$

12.

State the benchmarks you would use to approximate: $\sqrt[]{0.31}$

a)

$\sqrt[]{0.25}\ and\ \sqrt[]{0.36}$

b)

there are none

c)

$\sqrt[]{0.25}$

d)

$\sqrt[]{0.36}$

13.

State the benchmarks you would use to approximate: $\sqrt[]{86.5}$

a)

$\sqrt[]{81}\ and\ \sqrt[]{100}$

b)

there are none

c)

$\sqrt[]{81}\ \ only$

d)

$\sqrt[]{100}\ \ only$

14.

What approximation is the most reasonable for the following: $\sqrt[]{126}$

a)

11.1 or 11.2

b)

11.4 or 11.5

c)

11.6 or 11.7

d)

11.8 or 11.9

15.

What approximation is the most reasonable for the following: $\sqrt[]{3.21}$

a)

0.171 and 0.172

b)

0.174 and 0.175

c)

0.176 and 0.177

d)

0.178 and 0.179

16.

What approximation is the most reasonable for the following: $\sqrt[]{\frac{50}{220}}$

a)

$\frac{7}{15}$

b)

$\frac{25}{110}$

c)

$\frac{5}{22}$

d)

none of these

17.

$\sqrt{54}$ is between which two integers

a)

3 and 4

b)

4 and 5

c)

8 and 9

d)

7 and 8

18.

$\sqrt{81}$

a)

40.5

b)

9

c)

$\sqrt{9}$

19.

What is the proper name for this symbol: √

a)

radicand

b)

radical

c)

cube root

d)

index

20.

√49

a)

7

b)

7²

c)

14²

d)

14

21.

√63 is between which two perfect squares?

a)

7 and 8

b)

8 and 9

c)

6 and 7

d)

9 and 10

22.

√134 is between which two perfect squares?

a)

11 and 12

b)

10 and 11

c)

9 and 10

d)

8 and 9

23.

√98 is between which two perfect squares?

a)

9 and 10

b)

10 and 11

c)

11 and 12

d)

8 and 9

24.

√27 is between which two perfect squares?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

4 and 5

25.

√134 is approximately ...

a)

≈ 11.6

b)

≈ 11.5

c)

≈ 11.4

d)

≈ 11.7

26.

√27 written as a mixed number is ...

a)

5 and 2/11

b)

5 and 11/12

c)

5.18

d)

5.2

27.

√91 is between which two perfect squares?

a)

9 and 10

b)

8 and 9

c)

10 and 11

d)

7 and 8

28.

√11 is equivalent to which of the following?

a)

Three and two sevenths, 3.28, 3.3

b)

Three and two sevenths, 3.39, 3.3

c)

Three and two sevenths, 3.22, 3.2

d)

Three and two sevenths, 3.29, 3.2

29.

√107 is equivalent to which of the following?

a)

Ten and one third, 10.33, 10.3

b)

Ten and one third, 10.34, 10.3

c)

Ten and one third, 10.43, 10.3

d)

Ten and one third, 10.44, 10.4

30.

For this square root, name the two closest

perfect squares and their square roots √111

a)

81 and 100,9 and 10

b)

100 and 121, 10 and 11

c)

121 and 81,11 and 9

31.

In this triangle, determine the

unknown length.

a)

6

b)

2

c)

3

32.

In this triangle, determine the

unknown length.

a)

29.7

b)

15

c)

19

Estimating Roots

Total questions: 32

Worksheet time: 2hrs 53mins

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