Exercise 6.3

1. Find the square root of the following numbers by division method.

(i) 1089

Solution:

1089 =

(ii) 2304

Solution:

2304 =

(iii) 7744

Solution:

7744 =

(iv) 6084

Solution:

6084 =

(v) 9025

Solution:

9025 =

2. Find the square root of the following decimal numbers.

(i) 2.56

Solution:

2.56 =

(ii) 18.49

Solution:

18.49 =

(iii) 68.89

Solution:

68.89 =

(iv) 84.64

Solution:

84.64 =

3. Find the least number that is to be subtracted from 4000 to make it perfect square.

Solution:

Find the square root of 4000 = .

The square of 63 is .

The least number to be subtracted is - = .

4. Find the length of the side of a square whose area is 4489 sq.cm.

Solution:

Side of the square = Area = 4489 = cm.

5. A gardener wishes to plant 8289 plants in the form of a square and found that there were 8 plants left. How many plants were planted in each row?

Solution:

Number of plants actually arranged in a square = - =

Number of plants in each row = 8281 = .

6. Find the least perfect square with four digits.

Solution:

The smallest four-digit number is and 1000 ≈ 31.630.06.

The next whole number is . 322 = .

7. Find the least number which must be added to 6412 to make it a perfect square?

Solution:

6412 ≈ and the next whole number is .

812 =

The least number to be added is - = .

8. Estimate the value of the following numbers to the nearest whole number

(i) 97

Solution:

97 ≈ 100 = .

So, 97 ≈ .

(ii) 250

Solution:

250 is between 225 = and 256 = .

It's closer to . So, 250 ≈ .

(iii) 780

Solution:

780 is between 729 = and 784 = .

It's closer to . So, 780 ≈ .