What is the value of ((√15)²)?
Answer and explanation
Correct answer: 15
The principal square root √15 is the non-negative number whose square is 15. Therefore the inverse relationship between squaring and taking the principal square root gives (√15)² = 15. More generally, for every non-negative real number a, (√a)² = a. Hence option A is correct. It is important not to square 15 again: 225 would be 15², not the square of √15. Option B doubles the number, and option D applies an unrelated product rule. Because 15 is positive, there is no issue involving the sign or the distinction between √(x²) and (√x)²; the latter directly returns x here.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The principal square root √15 is the non-negative number whose square is 15. Therefore the inverse relationship between squaring and taking the principal square root gives (√15)² = 15. More generally, for every non-negative real number a, (√a)² = a. Hence option A is correct. It is important not to square 15 again: 225 would be 15², not the square of √15. Option B doubles the number, and option D applies an unrelated product rule. Because 15 is positive, there is no issue involving the sign or the distinction between √(x²) and (√x)²; the latter directly returns x here.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Real Numbers.
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