Squares and Square Roots (Class 8 Mathematics)

Understand perfect squares, square roots, and their properties. Learn estimation techniques and applications in geometry.

Squares and Square Roots (Class 8 Mathematics)

Understand perfect squares, square roots, and their properties. Learn estimation techniques and applications in geometry.

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TL;DR: Understand perfect squares, square roots, and their properties. Learn estimation techniques and applications in geometry.

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Understand perfect squares, square roots, and their properties. Learn estimation techniques and applications in geometry.

Squares and Square Roots MCQs with Answers & Explanations

Q1. What is a perfect square?

  1. A number divisible by 2
  2. The product of an integer with itself ✓ (correct)
  3. A number greater than 100
  4. Any even number

Explanation: A perfect square is a number obtained by multiplying an integer by itself. For example, 9 = 3 × 3, 16 = 4 × 4. Symbolically, n² is a perfect square.

Q2. Which of the following is a perfect square?

  1. 90
  2. 50
  3. 64 ✓ (correct)
  4. 80

Explanation: 64 = 8 × 8. So 64 is a perfect square. 50, 80, and 90 are not perfect squares.

Q3. What is √49?

  1. 24.5
  2. 14
  3. 49
  4. 7 ✓ (correct)

Explanation: √49 = 7 because 7 × 7 = 49. The square root finds the number that when multiplied by itself gives the radicand.

Q4. What is the square of 12?

  1. 144 ✓ (correct)
  2. 24
  3. 120
  4. 6

Explanation: 12² = 12 × 12 = 144. Squaring means multiplying a number by itself.

Q5. Simplify √16 + √9

  1. 5
  2. 7 ✓ (correct)
  3. 12
  4. 25

Explanation: √16 = 4 and √9 = 3. So √16 + √9 = 4 + 3 = 7.

Q6. Is √50 a rational or irrational number?

  1. Rational
  2. Neither
  3. Irrational ✓ (correct)
  4. Both

Explanation: √50 is irrational because 50 is not a perfect square. √50 = √(25×2) = 5√2, which cannot be expressed as p/q.

Q7. What is the value of √(100/25)?

  1. 10
  2. 5
  3. 4
  4. 2 ✓ (correct)

Explanation: √(100/25) = √100 / √25 = 10 / 5 = 2.

Q8. Estimate √85 (without calculator)

  1. 9.2 ✓ (correct)
  2. 10
  3. 8
  4. 9

Explanation: 9² = 81 and 10² = 100. Since 85 is closer to 81, √85 is approximately 9.2.

Q9. What is (-8)²?

  1. -64
  2. 64 ✓ (correct)
  3. -16
  4. 16

Explanation: (-8)² = (-8) × (-8) = 64. The square of a negative number is always positive.

Q10. What is the difference between √64 and ∛64?

  1. √64 is irrational
  2. √64 = 4, ∛64 = 8
  3. √64 = 8, ∛64 = 4 ✓ (correct)
  4. Both are same

Explanation: √64 (square root) = 8 because 8² = 64. ∛64 (cube root) = 4 because 4³ = 64. They are different operations.

Frequently Asked Questions

How can I estimate square roots of non-perfect squares?

Find the nearest perfect squares on both sides. For √85: since 81 < 85 < 100, we know 9 < √85 < 10. Then refine by checking values between 9 and 10.

Why is the square of a negative number positive?

Because we multiply the negative number by itself: (-5) × (-5) = positive 25. Negative times negative always equals positive.

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