Tiêu đề 6. SQUARES AND SQUARE ROOTS (Explanations).pdf ✅

√625 = 25 20.5 5 × 5 = 25 21.8, 15, 17 22.8.9 The square root of 79.21 is 8.9 23.Both A and R are true and R is the correct explanation of A. 24.81 2 25.2222 2222 as it has 2 in the end. 26.8, 15, 17 The general form of Pythagorean triplets is 2m, m 2 - 1, m 2+ 1 Given, 2m = 8 So, m = 4 m 2 - 1 = 4 2 - 1 = 16 - 1 = 15 m 2+ 1 = 4 2+ 1 = 16 + 1 = 17 27.n 2 28.9 29.Both A and R are true and R is the correct explanation of A. 30.Both A and R are true and R is the correct explanation of A. 31.4 32.34 Question should be read as: Non perfect square nunbers between 17 2 and 18 2 17 = n 18 = n + 1 (question for finding, non perfect square nunbers between 17 2 and 18 2 = 2n) ∴ non perfect square nunbers between 17 2and 18 2 = 2n = 2 × 17 = 34 33.1.6 34.Both A and R are true and R is the correct explanation of A. 35.10 √100 = 10 36.2116 We know that any number cannot be a perfect square if the ones place of the number are 2, 3, 7 and 8. So 1832, 1368 and 2357 cannot be a perfect square. Therefore, 2116 can be a perfect square as it ends with a digit 6. 37.2092 Solutiobn: If a number has 1 or 9 in the unit’s place, then its square ends in 1. 38.40 + 41 9 2 − 1 2 = 40, 5 2 + 1 2 = 41 39.62 2 The unit place of the square of 14 = 4 2 = 16 = 6 The unit place of the square of 62 - 2 2 = 4 [∵ 2 2 = 4] The unit place of square of 27 = 7 2 = 49 = 9 The unit place of the square of 35 = 5 2 = 52 = 5 Clearly, 62 2 has 4 at the unit's place. 40.m3 Given, m is the cube root of n, i.e. m = √n 3 ⇒ m = (n) 1 3 ⇒ m3 = (n) 3 3 [taking cube on both sides] ∴ m3 = n 41.1001 42.Both A and R are true and R is the correct explanation of A. 43.2 n = 3, n 2 = 2 44.1 1 × 1 = 1 45.900 46.0.45 47.5478 5478 as it has 8 at in the end. 48.169 49.Both A and R are true and R is the correct explanation of A.

85.A is false but R is true. 86.84 87.23 88.12 + 13 5 2 − 1 2 = 12, 5 2 + 1 2 = 13 89.1 We know that, it a number is ending in 1 or 9 in the unit's place, then its square ends in 1. The number ending in 9, will have the unit's place of its square as 1. [∵ 9 × 9 = 81] 90.10 The natural numbers lying between 5 2 and 6 2 , i.e. between 25 and 36 are 26, 27, 28, 29, 30, 31, 32, 33, 34 and 35. Hence, 10 natural numbers lie between 5 2 and 6 2 . 91.Both A and R are true and R is the correct explanation of A. 92.A is false but R is true. 93.69 2 123 2 =15129 so, the units place of the square of 123 = 9.69 2= 4761 so, the units place of the square of 69 = 1.34 2=1156 so, the units place of the square of 34 = 6. 37 2= 1369 so, the units place of the square of 37 = 9. We can see that, (69) 2have 1 at the units place. Alternate Method: If a number has 1 or 9 in the unit's place, then its square ends in 1. 94.49 49 is a perfect square. 49 = 7 × 7 = 7 2 95.25 From question, √576 + √2401 = √576 + 49 [since square root of 2401 = 49] = √625 = 25 [since square root of 625 = 29] 96.8, 15, 17 If we take x 2 + 1 = 17 So, x 2 = 16 ⇒ x = 4 Therefore, 2x = 8 and x 2 - 1 = (4) 2 - 1 = 16 - 1 = 15 Therefore, the required triplet is 8, 15 and 17. 97.6 98.9 2025 = 3 × 3 × 5 × 5 × 9 Here, prime factor 9 has no pair. Therefore 2025 must be divided by 9 to make it a perfect square. ∴ 2025 9 = 225 which is the square. 99.55 100.1112 101.4 Number of zeros at the end of the number 100 = 2 ∴ Number of zeros at the end of the square of the number 100 = 2 × 2 = 4 102.20 103.25 104.5 45 × 5 = 225 = 15 2 105.4 Finding the square root of 15370 by division method We get Remainder = 261 Now (123) 2 = 15129 and (124) 2 = 15379 The least number to be added = 15129 - 15379 = 6 106.A is false but R is true 107.1 9 × 9 = 81 108.6 109.A is false but R is true. 110.4 2 × 2 = 4 111.3 112.9 7 × 7 = 49 113.Both A and R are true and R is the correct explanation of A. 114.Both A and R are true and R is the correct explanation of A. 115.16 2 × 8 = 16 116.3 n = 5, n + 1 2 = 3 117.Both A and R are true and R is the correct explanation of A.