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Exercise 0.4, , Find the square roots of each of the following numbers by Division method:, , Question 1:, (i) 2304, (iii) 3481, (v) 3249, (vii) 5776, (ix) 576, (xi) 3136, € Answer 1:, (i) 2304, , Hence, the square root of 2304 is 48., , (ii) 4489, , Hence, the square root of 4489 is 67., , (iii) 3481, , Hence, the square root of 3481 is 59., , (iv) 529, , Hence, the square root of 529 is 23., , (v) 3249, , Hence, the square root of 3249 is 57., , (ii), (iv), (vi), (viii), (x), (xii), , 4489, 529, 1369, 7921, 1024, 900, , , , 48, 4 2304, - 16, 88 704, - 704, 0, 67, 6 44 89, - 36, 127 889, ~ 889, 0, 59, 5 3481, | - 25, 109981, - 981, 0, 23, 2 529, -4, 43 129, -129, 0, 57, 5 3249, = 25, 107.749, - 749

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(vi) 1369, , Hence, the square root of 1369 is 37., , (vii) 5776, , Hence, the square root of 5776 is 76., , (viii) 7921, , Hence, the square root of 7921 is 89,, , (ix) 576, , Hence, the square root of 576is 24., , (x) 1024, , Hence, the square root of 1024 is 32., , (xi) 3136, , Hence, the square root of 3136 is 56., , , , , , , , 37, 3 1369, -9, 67 469, ~ 469, 0, 76, 7 57 76, - 49, 146 876, ~ 876, 0, 89, 8 7921, _- 64, 169 1521, ~ 1521, 0, 24, 2 576, ~4, 44 176, -176, 0, 32, 3 10 24, = 9, 62 124, - 124, 0, 56, 5 31 36, = 25, 106 636, - 636

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(xii) 900, , 30, Hence, the square root of 900 is 30. 3 : 00, 00 000, - 000, Question 2: 0, , Find the number of digits in the square root of each of the following numbers (without, any calculation):, , (i) 64 (ii) =-144, (iii) 4489 (iv) 27225, (v) 390625, € Answer 2:, (i) Here, 64 contains two digits which is even., Therefore, number of digits in square root = 37 5 =1, (ii) Here, 144 contains three digits which is odd., Therefore, number of digits in square root = ae = = ; =2, (iv) Here, 4489 contains four digits which is even., Therefore, number of digits in square root = ; = ; =2, , (v) Here, 390625 contains six digits which is even., Therefore, number of digits in square root = fe 5 =3, , , , 2, Question 3:, Find the square root of the following decimal numbers:, (i) 2.56 (ii) 7.29, (iii) 51.84 (iv) 42.25, (v) 31.36, € Answer 3:, (i) 2.56 __j| 16 |, 1) 2.56, Hence, the square root of 2.56 is 1.6. wa, 26 156, - 156, 0, (ii) 7.29 2.7, 2 7.29, Hence, the square root of 7.29 is 2.7. -4, 47 329, - 329

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(iii) 51.84 72, , 7 = 5, Hence, the square root of 51.84 is 7.2. : ; - 84, 142 284, — 284, 0, 6.5, (iv) 42.25 6 42.25, - 36, Hence, the square root of 42.25 is 6.5. 125 625, | - 625, 0, 5.6, (vy) 31.36 S| 31.36, = - 25, Hence, the square root of 31.36 is 5.6. 106 oo, 0, Question 4:, , Find the least number which must be subtracted from each of the following numbers so, as to get a perfect square. Also, find the square root of the perfect square so obtained:, , (i) 402 (ii) 1989, , (iii) 3250 (iv) 825, , (v) 4000, , €. Answer 4:, , (i) 402 20, We know that, if we subtract the remainder from the ==, number, we get a perfect square. 2 40, Here, we get remainder 2. -4, Therefore 2 must be subtracted from 402 to get a 40 02, perfect square. - 00, , . 402 -2=400 2, Hence, the square root of 400 is 20., 20, 2 400, -4, 00 00, - 00, , 0

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(ii), , (iii), , (iv), , 1989, We know that, if we subtract the remainder from the, number, we get a perfect square., Here, we get remainder 53. Therefore 53 must be, subtracted from 1989 to get a perfect square., , 1989 - 53 = 1936, , Hence, the square root of 1936 is 44., , , , 44, 4 19 36, - 16, 84 = 336, - 336, , 0, , 3250, We know that, if we subtract the remainder from the, number, we get a perfect square., Here, we get remainder 1. Therefore 1 must be, subtracted from 3250 to get a perfect square., , 3250 -1=3249, , Hence, the square root of 3249 is 57., , 57, 5 32 49, | ~25, 107 749, = 749, 0, , 825, We know that, if we subtract the remainder from the, number, we get a perfect square., Here, we get remainder 41. Therefore 41 must be, subtracted from 825 to get a perfect square., , 825 - 41 = 784, , Hence, the square root of 784 is 28., , 28, 2 734, -4, 48 384, - 384, , 0, , 44, 4 19 89, | - 16, 84 389, - 336, 53, 57, 5 32 50, = 25, 107.750, = 749, 1, 28, 2 325, ond, 48 425, - 384, 41