10) 278784. 5) 145161. brightness_4 We use that Thus, Square root of 17. Since, 441 ends with ‘1’ it can be a perfect square number. Based on the fact mentioned above, repetitive subtraction of odd numbers starting from 1, until N becomes 0 needs to be performed. 4) 474721. Solution: Question 10. Ex 6.3, 3 Find the square roots of 100 and 169 by the method of repeated subtraction. (ii) 11² Find the square root by prime factorisation method. The steps to find the square root of 81 is: 81 – 1 = 80; 80 – 3 = 77; 77 – 5 = 72; 72 – 7 = 65; 65 – 9 = 56; 56 – 11 = 45; 45 – 13 = 32; 32 – 15 = 17; 17 – 17 = 0 Find the least number by which 1800 should be multiplied so that it becomes a perfect square. iv. By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? Question 12. As we know that every square number is the sum of consecutive odd natural numbers starting from 1, so we can find the square root by doing opposite because root is the inverse of the square. The square root of a number can be calculated by repeated subtraction method provided the number is an integer square number. (iv) 90 Step 1 : Separate the number into two digits (i. e 7 – 84) and Identify the lost digit of the number. \(\sqrt{169}\) = 13, Question 14. 7056 = 2² × 2² × 7² × 3² How do we find square root of numbers? Find a Pythagorean triplet whose (i) 144 (ii) 256 (iii) 784 Solution: (i) 144 Step 1: 144 – 1 = 143 Step 2: 143 – 3 = 140 Step 3: 140 – 5 = 135 Step 4: 135 – 7 = 128 Step 5: 128 – 9 = 119 Step 6: 119 – 11 = 108 Step 7: 108 – 13 = 95 Step 8: 95 – … 6.16 finding square root through prime factorisation part -1. 6.19 Finding square root through long division method … Finding the Square Root of Numbers. Squares and Square Roots . We know that 2m, m² – 1, m² + 1 form a Pythagorean triplet. ∴ \(\sqrt{3600}\) = 60. Find the smallest number by which 10985 should be divided so that the quotient is a perfect square. Square roots of decimal numbers by division method - law. ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 Question 1. (iii) 784 80 - 3 = 77. ∴ When we divide 10985 by 65 we get quotient 169. (ii) 441 Properties of a Square Root The perfect square exists only with the perfect square. v. The number of perfect square numbers between 300 and 500 is ………… 6.18 home work Exercise 6.3. There are multiple ways to find the square of the numbers. Solution: From 100, we subtract successive odd numbers starting from 1 as under: From 169, we subtract successive odd numbers starting from 1 as under: Ex 6.3 Class 8 Maths Question 4. Examine if each of the following is a perfect square: ∴ LCM of 8, 12, 15 is (4 × 3 × 2 × 5) = 120 The square root of 100 could be 10 or -10. Finding square root of a number by repeated subtraction method:-Repeated subtraction is a method of subtracting the equal number of … 72 - 7 = 65. ∴ The required Pythagorean triplet is (10, 24, 26). Solution: Step 2: 8 - 3 = 5. v. False. m² = 8 × 8 Let us find the square root of 104976 step by step using long division method. We get 0 in the 8th step. As you can see that given number 9 was repeatedly subtracted by successive odd numbers (starting from 1) and we get zero in third step. Solution: 190 = 2 × 5 × 19 (ii) If a number ends with 2, its square ends with 4. Study the following table […] Solution: Question 5. 5) 145161. Hence 1089 is a perfect square. Step 12: 135 – 23 = 112 The square root of a negative number is undefined. 9025 = 5 × 5 × 19 × 19 Solution: Translating the word problems in to algebraic expressions. 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