Estimate the value of the following to the nearest whole number :- 1) Square root of 80 2) Square root of 1000 3) Square root of 350 4) Square root of 500

Answer : 

1 ) Estimate $\sqrt{80}$ to the nearest whole number.

First list some perfect squares and look for the whole numbers near by 81.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, …

Observe that 80 lies between the perfect squares 64 and 81. That is, 64 < 80 < 81.

Now find the square root of each number.

$\sqrt{64}$  <  $\sqrt{80}$  < $\sqrt{81}$

So,  is between 8 and 9.

Since 80 is much closer to 80 than to 64, the best whole number estimate is 9 .                ( Ans )

​2 ) Estimate $\sqrt{1000}$ to the nearest whole number.

First list some perfect squares and look for the whole numbers near by 1000.

30² = 900

31² = 961 

32² = 1024


Observe that 1000 lies between the perfect squares 961 and 1024. That is, 961 < 1000 < 1024 .

Now find the square root of each number.

$\sqrt{961}$  <  $\sqrt{1000}$ < $\sqrt{1024}$

So,  is between 31 and 32.

Since 1000 is much closer to 1024 than to 961, the best whole number estimate is 32 .                ( Ans )


3 ) Estimate $\sqrt{350}$ to the nearest whole number.

First list some perfect squares and look for the whole numbers near by 350.

15²  = 225

16²  = 256 

17²  = 289

18²  = 324

19²  = 361


Observe that 350 lies between the perfect squares 324 and 361. That is, 324 < 350 < 361 .

Now find the square root of each number.

$\sqrt{324}$  <  $\sqrt{350}$ < $\sqrt{361}$

So,  is between 18 and 19.

Since 350 is much closer to 361 than to 324, the best whole number estimate is 19 .                ( Ans )


4 ) Estimate $\sqrt{500}$ to the nearest whole number.

First list some perfect squares and look for the whole numbers near by 500.

20² = 400

21² = 441

22² = 484

23² = 529


Observe that 500 lies between the perfect squares 484 and 529. That is, 484 < 500 < 529 .

Now find the square root of each number.

$\sqrt{484}$  <  $\sqrt{500}$ < $\sqrt{529}$

So,  is between 22 and 23.

Since 500 is much closer to 484 than to 529, the best whole number estimate is 22 .                ( Ans )