Breath Math

The Square Root Exercise 1.1.2 belongs to the chapter Square Root.

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Square Root Exercise 1.1.2

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

1. 5329

Solution:

Therefore √(5329) = 73

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2. 18769

Solution:

Therefore √(18769) = 137

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3. 28224

Solution:

Therefore √(28224) = 168

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4. 186624

Solution:

Therefore √(186624) = 432

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2. 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.

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2. 12675

Solution:

112² = 12544 < 12675 < 12769 = 113²

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

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3. 88417

Solution:

297² = 88209 < 88417 < 88804 = 298²

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

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4. 123456

Solution:

351² = 123201 < 123456 < 123904 = 352²

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

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3. 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.

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2. 4321

Solution:

65² = 4225 < 4321 < 4356 = 66²

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

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3. 34567

Solution:

185² = 34225 < 34567 < 34596 = 186²

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

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4. 109876

Solution:

331² = 109561 < 109876 < 110224 = 332²

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

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4. 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.

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2. 56789

Solution:

238² = 56644 < 56789 < 57121 = 239²

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

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3. 88888

Solution:

298² = 88804 < 88888 < 89401 = 299²

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

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4. 123456

Solution:

351² = 123201 < 123456 < 123904 = 352²

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

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5. 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.

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