# RS Aggarwal Class 8 Math Third Chapter Squares and Square Roots Exercise 3E Solution

## EXERCISE 3E

### Evaluate:

**(1) ****√576**

**(2) √1444**

**(3) √4489**

**(4) √6241**

**(5) √7056**

**(6) √9025**

**(7) √11449**

**(8) √14161**

**(9) √10404**

**(10) √17956**

**(11) √19600**

**(12) √92416**

**(13) Find the least number which must be subtracted from 2509 to make it a perfect square.**

Solution: Let us try to find the square root of 2509.

This shows that (50)^{2} is less than 2509 by 9.

Required perfect square number = (2509 – 9) = 2500.

And, √2500 = 50.

**(14) Find the least number which must be subtracted from 7581 to obtain a perfect square. Find this perfect square ant its square root.**

Solution: Let us try to find the square root of 7581.

This shows that (87)^{2} is less than 7581 by 12.

Required perfect square number = (7581 – 12) = 7569.

And, √7569 = 87.

**(15) Find the least number which must be added to 6203 to obtain a perfect square. Find this perfect square and its square root.**

Solution: We try to find the square root of 6203.

We observe here that (78)^{2} < 6203 < (79)^{2}.

The required number to be added = (79)^{2} – 6203 = (6241 – 6203) = 38.

Clearly, the required perfect square = 6241 and √6241 = 79.

**(16) Find the least number which must be added to 8400 to obtain a perfect square. Find this perfect square and its square root.**

Solution: We try to find the square root of 8400.

We observe here that (91)^{2} < 8400 < (92)^{2}.

The required number to be added = (92)^{2} – 8400 = (8464 – 8400) = 64.

Clearly, the required perfect square = 8464 and √8464 = 92.

**(17) Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.**

Solution: the least number of four digits = 1000, which is not a perfect square.

Now, we must find the least number which when added to 1000 gives a perfect square. This perfect square is required number.

Now, we find out the square root of 1000.

Clearly, (31)^{2} < 1000 < (32)^{2}_{.}

∴ The least number to be added = (32)^{2} – 1000 = (1024 – 1000) = 24.

Hence, the required number = (1000 + 24) = 1024.

Also, √1024 = 32.

**(18) Find the greatest number of five digits which is perfect square. Also find the square root of the number so obtained.**

Solution: the least number of four digits = 99999, which is not a perfect square.

Now, we must find the least number which when added to 99999 gives a perfect square. This perfect square is required number.

Now, we find out the square root of 99999.

Clearly, (316)^{2} < 99999 < (317)^{2}_{.}

∴ The least number to be added = (317)^{2} – 99999 = (100489 – 99999) = 490.

Hence, the required number = (99999 + 490) = 100489.

Also, √100489 = 317.

**(19) The area of a square field is 60025 m ^{2}. A man cycles along its boundary at 18 km/h. In how much time will he return to the starting point?**