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Important Questions

Squares and Square Roots

ICSE · Class 8 · Mathematics

Most important questions from Squares and Square Roots for ICSE Class 8 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

38 questions30 flashcards5 concepts

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38 Questions·
multiple choice

Sample Questions

1multiple choice
1 marks

Using the division method, what is √4761?

Show answer

69

Step 1: Group digits from right: 47 | 61. Step 2: Find largest number whose square ≤ 47. Since 6² = 36 ≤ 47 and 7² = 49 > 47, write 6 as quotient. Subtract 36 from 47, remainder = 11. Step 3: Bring down 61, new dividend = 1161. Double quotient: 2 × 6 = 12. Find digit d such that 12d × d ≤ 1161. Try d = 9: 129 × 9 = 1161. Perfect! Step 4: Subtract 1161 − 1161 = 0. Quotient = 69. Verify: 69 × 69 = 4761. ✓

2multiple choice
1 marks

The square root of 0.001225 is:

Show answer

0.035

Step 1: Write 0.001225 as a fraction: 1225/1000000. Step 2: Find √1225 and √1000000 separately. Step 3: 1225 = 5 × 5 × 7 × 7 = (5×7)² = 35², so √1225 = 35. Step 4: √1000000 = √(10^6) = 10^3 = 1000. Step 5: √(1225/1000000) = 35/1000 = 0.035. Verify: (0.035)² = 0.001225. ✓ Common mistake: Students often write 0.35 by forgetting the correct number of decimal places.

3multiple choice
1 marks

Which of the following numbers CANNOT be a perfect square?

Show answer

8000

Step 1: A perfect square ends in 0, 1, 4, 5, 6, or 9. Also, a number ending in an odd number of zeroes can NEVER be a perfect square. Step 2: 8000 ends in 3 zeroes (odd number of zeroes), so it cannot be a perfect square. Step 3: Check others — 1024 = 32², 2025 = 45², 4900 = 70² (ends in 2 zeroes which is even). Step 4: 8000 = 2^6 × 5^3 — the factor 5 appears 3 times (odd), so it cannot be a perfect square. Answer: 8000.

4multiple choice
1 marks

The square root of 2(7/9) is:

Show answer

1(2/3)

Step 1: Convert mixed fraction to improper fraction: 2(7/9) = (18+7)/9 = 25/9. Step 2: Apply rule: √(a/b) = √a / √b. So √(25/9) = √25 / √9. Step 3: √25 = 5 and √9 = 3. Step 4: √(25/9) = 5/3 = 1(2/3). Verify: (5/3)² = 25/9 = 2(7/9). ✓ Common mistake: Students sometimes try to find √2 and √(7/9) separately, which is incorrect.

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Frequently Asked Questions

What are the important topics in Squares and Square Roots for ICSE Class 8 Mathematics?
Key topics in Squares and Square Roots include Squares and Square Roots - Concept Overview, Squares and Square Roots – Complete Chapter Overview, Flowchart showing that squaring any number (positive or negative) always gives a positive result. These are the concepts ICSE Class 8 examiners draw on most — study them first, then practise related questions.
How to score full marks in Squares and Square Roots — ICSE Class 8 Mathematics?
Understand the core concepts first, then work through the 38 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Squares and Square Roots?
There are 38 practice questions available for Squares and Square Roots. These cover multiple question types including MCQs, short answer, and long answer questions.

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