What is √(16/25) equal to?
Answer and explanation
Correct answer: 4/5
The governing rule is that for positive numbers, √(a/b) = √a/√b, together with the convention that the radical denotes the principal, non-negative square root. Therefore √(16/25) = √16/√25 = 4/5. This is confirmed by squaring: (4/5)² = 16/25, and 4/5 is non-negative, so it is the principal square root. Thus option B is correct. Option A, 8/5, has square 64/25 and is too large. Option C is the original number inside the radical, not its square root. Option D, 5/4, is the reciprocal of the correct value. Since both 16 and 25 are perfect squares, the result is rational, even though the question belongs to work with square roots.
Frequently asked questions
What is the correct answer to this question?
4/5
Why is this the correct answer?
The governing rule is that for positive numbers, √(a/b) = √a/√b, together with the convention that the radical denotes the principal, non-negative square root. Therefore √(16/25) = √16/√25 = 4/5. This is confirmed by squaring: (4/5)² = 16/25, and 4/5 is non-negative, so it is the principal square root. Thus option B is correct. Option A, 8/5, has square 64/25 and is too large. Option C is the original number inside the radical, not its square root. Option D, 5/4, is the reciprocal of the correct value. Since both 16 and 25 are perfect squares, the result is rational, even though the question belongs to work with square roots.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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