Answer As explained in Properties of Square Numbers the square number is the sum of successive odd numbers starting from 1 and you can find the square root of a number by repeatedly subtracting successive odd numbers( which is also starting from 1) from the given square number, till you get zero. (i) 729We use prime factorization to find square root.Thus, 729 = 3 × 3 × 3 × 3 × 3 × 3Square root of 729 = 3 × 3 × 3 = 9 × 3 = 27 Ex 6.3, 4 Find the square roots of t Watch Queue Queue Question 1. 19. 72 - 7 = 65. 35 - 3 = 32. Repeated subtraction method is a method in which the number whose square root is to be determined is subtracted repeatedly by consecutive odd numbers till the difference obtained is zero. Join now. 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. (i) 36 Find the square roots of 100 and 169 by the method of repeated subtraction. Question 1. (ii) The first 99 odd natural numbers. let 2m = 10 How do we find square root of numbers? (iv) 3042 Or we can also write it as: √ 9 = 3. ∴ 784 is a perfect square. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. Only numbers ending with even number of zeros have square roots. iii. 9025 = 5 × 5 × 19 × 19 32 - 15 = 17. = 2 × 2 × 7 × 3 = 84 To find Square root,we subtract consecutive odd numbers from number till we obtain 0.Square root = Total numbers subtracted.Let’s take an exampleSuppose we need to find√81Square root of√8181 − 1 = 8080 − 3 = 7777 − 5 = 7272 − 7 = 6565 − 9 = 5656 … Finding square root of 100 by using repeated subtraction: (i) 100 – 1 … Find the square root of the following by repeated subtraction method. This video is unavailable. That is 324. Find the square root by prime factorisation method. Remainder when 17 power 23 is divided by 16. ∴ $$\sqrt{1156}$$ = $$(\sqrt{2×17})^{2}$$ = 2 × 17 = 34 (7, 24, 25) is a Pythagorean triplet. Let us consider another example to find the square root of 81 by repeated subtraction. (ii) 6, 9, 27, 36 The square of the number is equal to the number or frequency of subtraction performed on the number. ∴ 3600 = 1800 × 2 Sum of all three digit numbers divisible by 6. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. Find the square roots of the following numbers by prime factorisation method: v. The number of perfect square numbers between 300 and 500 is ………… (ii) 34567 Consider the following steps to find the square root of 784. Find the square roots of 100 and 169 by the method of repeated subtraction. Finding Square Root – Repeated Subtraction method To find the square root of a given number, we subtract consecutive odd numbers (starting from 1) from it till we get 0. m² + 1 = 5² + 1 = 25 + 1 = 26 ∴ Sum of 99 odd natural numbers = 99² = 99 × 99 = 9801. (i) 725 (iii) 784 Find the square roots of 100 and 169 sby the method of repeated Subtraction.... give correct answer or wrong answer will be reported See answer ... Answer: Square of 100 is 10 and 169 is 13. aimenmalek8670 aimenmalek8670 Answer: square root of 100 is 10. square root of 169 is 13. Step 9: 192 – 17 = 175 Through Repeated Subtraction. Step 15: 60 – 29 = 31 (iii) 1849 Sum of first n consecutive odd natural numbers = n² 190 = 2 × 5 × 19 v. The square root of 221 is 21. Translating the word problems in to algebraic expressions. ∴ 256 is a perfect square and $$\sqrt{256}$$ = 16, (iii) 784 Log in. 48 Find the square roots of 100 and 169 hy the method of repeated subtraction. Find the square root of the new number. 4761 = 3 × 3 × 23 × 23 Q.3 Find the square roots of 100 and 169 by the method of repeated subtraction. 3600 = 2² × 3² × 5² × 2² The area of a rectangle is 1936 sq. We can find square root of a number by repeatedly subtracting successive odd numbers starting from 1 from the given square number, till we get zero. 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Square root of 7056 is 86. 72 - 7 = 65. ii. Example 1: Find the square root of 81 using the repeated subtraction method. Here the factor 3 has no pair. 4) 474721. ∴ 2352 is not a perfect square. We know that the sum of first n odd natural numbers is n 2. (ii) 190 Solution: We have subtracted odd numbers starting from 1 repeatedly from 256. We will subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach $$0$$ The number of times we subtract is the square root of the given number. If the same number is repeatedly subtracted from another larger number until the remainder is zero or a number smaller than the number being subtracted, we can write that in … Step 22: 343 – 43 300 1089 = 3 × 3 × 11 × 11 = 33 × 33 In addition to giving a way to find square roots by hand, this method can be used if all you have is a cheap 4-function calculator. Solution: Question 2. ML Aggarwal Solutions for Class 8 Maths Chapter 3 Squares and Square Roots help students understand the types of methods to be followed in solving problems effortlessly. Step 2: 783 – 3 = 780 ∴ Ones’ digit in the square of 543 is 9. True We know that 2m, m² – 1, m² + 1 form a Pythagorean triplet. Long Division Method. Example 2: Now if we have to find the square root of 2, then it is difficult to find using factorisation method. (v) 6241 100 – 1 = 99  99 – … Click hereto get an answer to your question ️ Find the square root of the following number by Division method. Study the following table […] Solution: This proceeds as: Step 1: 9 - 1 = 8 Step 2: 8 - 3 = 5 Step 3: 5 - 5 = 0 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. 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. Is 2352 a perfect square? Solution: This proceeds as: Step 1: 9 - 1 = 8. This video is highly rated by Class 8 students and has been viewed 806 times. If a number ends with 5, its square ends with ………… Thus, square root of 36 by successive subtraction method is 6. L.C.M method to solve time and work problems. Therefore, 441 is a perfect square. Solution: Question 13. Step 5: 768 – 9 = 759 1156 = 2² × 17² i. $$\sqrt{3600}$$ = $$(\sqrt{2 × 3 × 5 × 2})^{2}$$ = 2 × 3 × 5 × 2 = 60 Find the smallest square number that is divisible by each of the following numbers: Express We will subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach $$0$$ The number of times we subtract is the square root of the given number. Methods to find square root: 1. 32 - 15 = 17. For each of the following numbers, find the smallest natural number by which it should be multiplied so as to get a perfect square. Transcript. Here the last factor 2 has no pair. Sep 26, 2020 - Repeated Subtraction Method - Square and Square Roots, Mathematics, CBSE Class 8 Class 8 Video | EduRev is made by best teachers of Class 8. v. False. 3. If the number is a perfect square then find its square root: (i) 121 (ii) 55 (iii) 36 (iv) 90 Solution: Question 2. ∴ 2352 × 3 = 2² × 2² × 7² × 3 × 3 3) 65536. ii. Solution: Save my name, email, and website in this browser for the next time I comment. Question 4. Find the square root of 144 by the method of repeated subtraction. A few popular methods used to find the square root of a number are: Guess and check Method. (ii) 11² Step 9: 80 – 17 = 63 We will see a few of the here. Solution: Using the method of repeated subtraction of consecutive odd numbers, we have (i) 100 – 1 = 99, 99 – 3 = 96, 96 – 5 = 91, 91 – 7 = 84, 84 – 9 = 75, 75 – 11 = 64, 64 – 13 = 51, 51 – 15 = 36, 36 – 17 = 19, 19 – 19 = 0 (Ten times repetition) Step 10: 703 – 19 = 684 From the above picture, finally we got the square root of 104976. (i) 1156 (ii) 720 iii. m² = 65 – 1 841 = 29 × 29 $$\sqrt{4761}$$ = $$(\sqrt{3 × 23})^{2}$$ We get 0 in the 12th step. Step 2 : Square root of 100. Solution: = (2 × 3 × 5 × 2)² Finding the Square Root of Numbers. (i) 10² and Let us find the square root of 104976 step by step using long division method. 10) 278784. 2, 3, 7, 8 The least number divisible by each of the numbers 8, 12, 15 is their L.C.M Is 9 as: step 1: find the square root of by! Roots: -Square root is the square roots of 100 and 169 by the method of subtraction. 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