1. Find .
- A9
- B8
- C40.5
- D18
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Answer: A) 9
9 × 9 = 81. So .
Class 8 Squares and Square Roots — 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.
2. For a Pythagorean triplet built from 2m, m² − 1, m² + 1, take m = 4. What is the largest member of the triplet?
- A17
- B18
- C34
- D16
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Answer: A) 17
With m = 4: 2m = 8, m² − 1 = 15, m² + 1 = 17. The triplet is (8, 15, 17), so the largest member is 17.
3. Find by prime factorisation.
- A95
- B115
- C210
- D105
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Answer: D) 105
11025 = 3² × 5² × 7² = (3 × 5 × 7)² = 105². So .
4. Find .
- A1.9
- B0.19
- C0.019
- D19
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Answer: B) 0.19
361 = 19², and 0.0361 has 4 decimal places, so its square root has 4 ÷ 2 = 2 decimal places: (check: 0.19 × 0.19 = 0.0361). The traps 1.9, 0.019 and 19 all misplace the decimal point — count the decimal places and halve them.
5. Which is larger, or 0.49?
- A0.49, because taking a square root always makes a number smaller
- BThey are exactly equal
- C, because it equals 0.07
- D, because it equals 0.7 and 0.7 > 0.49
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Answer: D) , because it equals 0.7 and 0.7 > 0.49
since 0.7 × 0.7 = 0.49, and 0.7 is larger than 0.49. A square root only shrinks a number that is greater than 1; for a number between 0 and 1 the root is LARGER than the number itself, which is why the first option fails. The option 0.07 misplaces the decimal point: 0.07² = 0.0049, not 0.49.
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