Class 8 Square Root by Long Division — practice questions with answers
Squares and Roots · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Using the long division method, find the square root of 529.
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Answer: B) 23
Pair from right: 5 29. Largest square <= 5 is 4 (2²), remainder 1. Bring down 29 -> 129. Double 2 = 4; find x with 4x*x <= 129: 43*3 = 129. So
529 = 23.
2. How many digits will the square root of 390625 have?
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Answer: B) 3
390625 has 6 digits (even). Number of digits in the square root = 6/2 = 3. (
390625 = 625.)
3. Find the square root of 1.5625 by long division.
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Answer: C) 1.25
Pair: 1 . 56 25. 1² = 1, rem 0 -> 56; 22*2 = 44, rem 12 -> 1225; double 12 = 24, 245*5 = 1225. So
1.5625 = 1.25.
4. A square plot in Nagpur has an area of 39.69 square metres.
Find the length of its side correct to one decimal place using long division.
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Answer: B) 6.3 m
Side =
39.69. Pair: 39 . 69. 6² = 36, rem 3 -> 369; double 6 = 12, 123*3 = 369, rem 0. So
39.69 = 6.3 m.
5. Find
7 correct to two decimal places using long division.
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Answer: C) 2.65
Pair: 7.00 00. 2² = 4, rem 3 -> 300; 46*6 = 276, rem 24 -> 2400; 525*5 = 2625 too big, 524*4 = 2096. Digits 2.645... rounds to 2.65 (2 d.p.).