ESTIMATING SQUARE ROOTS WORKSHEET

Estimate the values of the following square roots to the nearest whole number :

Question 1 :

√8

Question 2 :

√40

Question 3 :

√80

Question 4 :

√1000

Question 5 :

√172

Question 6 :

√5928

1. Answer :

√8

8 is not a perfect square.

Find the two perfect squares surrounding 8.

They are 4 and 9.

Then, we have

4 < 8 < 9

2² < 8 < 3²

Taking square root, we have

√2² < √8 < √3²

2 < √8 < 3

The value of √8 lies between 2 and 3. 

In the inequality 4 < 8 < 9, since 8 is closer to 9, the approximate value of √8 is 3.

2. Answer :

√40

40 is not a perfect square.

Find the two perfect squares surrounding 40.

They are 36 and 49.

Then, we have

36 < 40 < 49

6² < 40 < 7²

Taking square root, we have

√6² < √40 < √7²

6 < √40 < 7

The value of √40 lies between 6 and 7. 

In the inequality 36 < 40 < 49, since 40 is closer to 36, the approximate value of √40 is 6.

3. Answer :

√80

80 is not a perfect square.

Find the two perfect squares surrounding 80.

They are 64 and 81.

Then, we have

64 < 80 < 81

Taking square root,

√64 < √80 < √81

8 < √80 < 9

The value of √80 lies between 8 and 9. 

In the inequality 64 < 80 < 81, since 80 is closer to 81, the approximate value of √80 is 9.

4. Answer :

√1000

1000 is not a perfect square.

Find the two perfect squares surrounding 1000.

They are 961 and 1024.

Then, we have

961 < 1000 < 1024

Taking square root,

√961 < √1000 < √1024

31 < √1000 < 32

The value of √1000 lies between 31 and 32. 

In the inequality 961 < 1000 < 1024, since 1000 is closer to 1024, the approximate value of √1000 is 32.

5. Answer :

√172

172 is not a perfect square.

Find the two perfect squares surrounding 172.

They are 169 and 196.

Then, we have

169 < 172 < 196

Taking square root,

√169 < √172 < √196

13 < √172 < 14

The value of √172 lies between 13 and 14. 

In the inequality 169 < 172 < 196, since 172 is closer to 169, the approximate value of √172 is 13.

6. Answer :

√5928

5928 is not a perfect square.

Find the two perfect squares surrounding 5928.

They are 5776 and 5929.

Then, we have

5776 < 5928 < 5929

Taking square root,

√5776 < √5928 < √5929

76 < √5928 < 77

The value of √5928 lies between 76 and 77. 

In the inequality 5776 < 5928 < 5929, since 5928 is closer to 5929, the approximate value of √5928 is 77.

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