Squares and Square Roots — Previous Year Questions (Class 8 Mathematics)
Understand perfect squares, square roots, and their properties. Learn estimation and calculation techniques.
TL;DR: Understand perfect squares, square roots, and their properties. Learn estimation and calculation techniques.
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Understand perfect squares, square roots, and their properties. Learn estimation and calculation techniques.
Squares and Square Roots — Previous Year Questions with Solutions
Q (2023, 2 marks): Find the square of 15 and the square root of 225.
Answer: Square of 15: 15^2 = 15 × 15 = 225
Square root of 225: sqrt(225) = 15
Note: 15 and sqrt(225) are inverses of each other.
Q (2022, 2 marks): Is 50 a perfect square? Justify your answer.
Answer: No, 50 is not a perfect square.
Reason: sqrt(50) ≈ 7.07 (not an integer)
7^2 = 49; 8^2 = 64
Since 50 lies between 49 and 64, it is not a perfect square.
Q (2023, 2 marks): Find sqrt(1.44)
Answer: sqrt(1.44) = 1.2
Verification: 1.2 × 1.2 = 1.44
Q (2022, 3 marks): Calculate sqrt(144 + 25) and compare with sqrt(144) + sqrt(25).
Answer: sqrt(144 + 25) = sqrt(169) = 13
sqrt(144) + sqrt(25) = 12 + 5 = 17
Comparison: 13 ≠ 17
Note: sqrt(a + b) ≠ sqrt(a) + sqrt(b). Squareroot is not distributive over addition.
Q (2023, 3 marks): Using prime factorization, find sqrt(3600).
Answer: Prime factorization of 3600:
3600 = 36 × 100 = (6^2) × (10^2) = (2 × 3)^2 × (2 × 5)^2
3600 = 2^4 × 3^2 × 5^2
sqrt(3600) = 2^2 × 3 × 5 = 4 × 3 × 5 = 60
Verification: 60 × 60 = 3600
Q (2022, 2 marks): Estimate sqrt(50) between two consecutive integers.
Answer: 7^2 = 49
8^2 = 64
Since 49 < 50 < 64, therefore 7 < sqrt(50) < 8
Frequently Asked Questions
What is the relationship between squares and square roots?
Squares and square roots are inverse operations. If a^2 = b, then sqrt(b) = a. For example, 5^2 = 25 and sqrt(25) = 5.
Can a negative number have a square root?
In real numbers, no. The square root of a negative number is not defined in real numbers. For example, sqrt(-4) does not exist in real numbers because no real number squared gives a negative result. (In complex numbers, it is defined using imaginary unit i.)
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