Belongs to the unit Square Root

Exercise 1.1.2

- Find the square root of the following numbers by division method:

1. 5329

**Solution:**

Therefore √(5329) = 73

- 18769

**Solution:**

Therefore √(18769) = 137

- 28224

**Solution:**

Therefore √(28224) = 168

- 186624

**Solution:**

Therefore √(186624) = 432

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

1.6200

**Solution:**

78^{2} = 6084 < 6200 < 6241 = 79^{2}

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

- 12675

**Solution:**

112^{2} = 12544 < 12675 < 12769 = 113^{2}

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

- 88417

**Solution:**

297^{2} = 88209 < 88417 < 88804 = 298^{2}

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

- 123456

**Solution:**

351^{2} = 123201 < 123456 < 123904 = 352^{2}

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

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

1)1234

**Solution:**

35^{2} = 1225 < 1234 < 1296 = 36^{2}

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

- 4321

**Solution:**

65^{2} = 4225 < 4321 < 4356 = 66^{2}

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

- 34567

**Solution:**

185^{2} = 34225 < 34567 < 34596 = 186^{2}

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

- 109876

**Solution:**

331^{2} = 109561 < 109876 < 110224 = 332^{2}

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

- Find the consecutive perfect squares between which the following numbers lie:

1)4567

**Solution:**

67^{2} = 4489 < 4567 < 4624 = 68^{2}

So, the square root of 4567 lies between 67^{2} and 68^{2}.

- 56789

**Solution:**

238^{2} = 56644 < 56789 < 57121 = 239^{2}

So, the square root of 56789 lies between 238^{2} and 239^{2}.

- 88888

**Solution:**

298^{2} = 88804 < 88888 < 89401 = 299^{2}

So, the square root of 88888 lies between 298^{2} and 299^{2}.

- 123456

**Solution:**

351^{2} = 123201 < 123456 < 123904 = 352^{2}

So, the square root of 56789 lies between 351^{2} and 352^{2}.

- 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 154^{2} = 23715 sq. m.

He will lose 224 m^{2}.