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# 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: Therefore √(5329) = 73

1. 18769

Solution: Therefore √(18769) = 137

1. 28224

Solution: Therefore √(28224) = 168

1. 186624

Solution: Therefore √(186624) = 432

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

1.6200

Solution: 782 = 6084 < 6200 < 6241 = 792

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

1. 12675

Solution: 1122 = 12544 < 12675 < 12769 = 1132

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

1. 88417

Solution: 2972 = 88209 < 88417 < 88804 = 2982

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

1. 123456

Solution: 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: 352 = 1225 < 1234 < 1296 = 362

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

1. 4321

Solution: 652 = 4225 < 4321 < 4356 = 662

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

1. 34567

Solution: 1852 = 34225 < 34567 < 34596 = 1862

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

1. 109876

Solution: 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: 672 = 4489 < 4567 < 4624 = 682

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

1. 56789

Solution: 2382 = 56644 < 56789 < 57121 = 2392

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

1. 88888

Solution: 2982 = 88804 < 88888 < 89401 = 2992

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

1. 123456

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

He will lose 224 m2.