Square root Exercise 1.1.2

Belongs to the unit Square Root

Exercise 1.1.2

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

1. 5329

Solution:

10

Therefore √(5329) = 73

  1. 18769

Solution:

11

Therefore √(18769) = 137

  1. 28224

Solution:

12.png

Therefore √(28224) = 168

  1. 186624

Solution:

13

Therefore √(186624) = 432

 

  1. Find the least number to be subtracted from the following numbers to get a perfect square.

1.6200

Solution:

14

782 = 6084 < 6200 < 6241 = 792

So, we have to add 41 to get the next perfect square.

 

  1. 12675

Solution:

15

1122 = 12544 < 12675 < 12769 = 1132

So, we have to add 94 to get the next perfect square.

 

  1. 88417

Solution:

16

2972 = 88209 < 88417 < 88804 = 2982

So, we have to add 387 to get the next perfect square.

 

  1. 123456

Solution:

17

3512 = 123201 < 123456 < 123904 = 3522

So, we have to add 448 to get the next perfect square.

 

  1. Find the least number to be subtracted from the following numbers to get a perfect square.

1)1234

Solution:

18

352 = 1225 < 1234 < 1296 = 362

So, we have to subtract  9 to get the next perfect square.

 

  1. 4321

Solution:

19.png

652 = 4225 < 4321 < 4356 = 662

So, we have to subtract  96 to get the next perfect square.

 

  1. 34567

Solution:

20

1852 = 34225 < 34567 < 34596 = 1862

So, we have to subtract  342 to get the next perfect square.

 

  1. 109876

Solution:

21

3312 = 109561 < 109876 < 110224 = 3322

So, we have to subtract  315 to get the next perfect square.

 

  1. Find the consecutive perfect squares between which the following numbers lie:

1)4567

Solution:

21

672 = 4489 < 4567 < 4624 = 682

So, the square root of 4567 lies between 672 and 682.

 

  1. 56789

Solution:

22

2382 = 56644 < 56789 < 57121 = 2392

So, the square root of 56789 lies between 2382 and 2392.

 

  1. 88888

Solution:

23

2982 = 88804 < 88888 < 89401 = 2992

So, the square root of 88888 lies between 2982 and 2992.

 

  1. 123456

Solution:

24

3512 = 123201 < 123456 < 123904 = 3522

So, the square root of 56789 lies between 3512 and 3522.

 

  1. A person has three rectangular plots of dimensions 112 m x 54 m, 84 m x 68 m and 140 m x 87 m at different places. He wants to sell all of them and buy a square plot of integral length of maximum possible area approximately equal to the sum of these plots. What would be the dimensions of such a square plot? How much area he may have to lose?

Solution:

The area of the 3 rectangular plots is

(112 x 54) m = 6048 sq. m.

(84 x 68) m = 5712 sq. m.

(140 x 87) m = 12180 sq. m.

Total area = 23940 sq. m.

26

The area of the new square plot is 1542  = 23715 sq. m.

He will lose 224 m2.