The Square Root Exercise 1.1.2 belongs to the chapter Square Root.
Square Root Exercise 1.1.2
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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
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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.
- 12675
Solution:
1122 = 12544 < 12675 < 12769 = 1132
So, we have to add 94 to get the next perfect square.
- 88417
Solution:
2972 = 88209 < 88417 < 88804 = 2982
So, we have to add 387 to get the next perfect square.
- 123456
Solution:
3512 = 123201 < 123456 < 123904 = 3522
So, we have to add 448 to get the next perfect square.
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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.
- 4321
Solution:
652 = 4225 < 4321 < 4356 = 662
So, we have to subtract 96 to get the next perfect square.
- 34567
Solution:
1852 = 34225 < 34567 < 34596 = 1862
So, we have to subtract 342 to get the next perfect square.
- 109876
Solution:
3312 = 109561 < 109876 < 110224 = 3322
So, we have to subtract 315 to get the next perfect square.
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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.
- 56789
Solution:
2382 = 56644 < 56789 < 57121 = 2392
So, the square root of 56789 lies between 2382 and 2392.
- 88888
Solution:
2982 = 88804 < 88888 < 89401 = 2992
So, the square root of 88888 lies between 2982 and 2992.
- 123456
Solution:
3512 = 123201 < 123456 < 123904 = 3522
So, the square root of 56789 lies between 3512 and 3522.
- 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.