Which statement is correct when comparing √2 and √3?
Answer and explanation
Correct answer: √2 < √3
The governing concept is that the square-root function is increasing for non-negative numbers. Because 2 < 3, taking their principal square roots preserves the inequality, giving √2 < √3. This can also be checked by approximation: √2 is about 1.414 and √3 is about 1.732. Therefore option C is correct. The two numbers cannot be equal because equal non-negative square roots would have equal squares, whereas 2 and 3 are different. Option A reverses the valid inequality. Option D is also false because neither 2 nor 3 is a perfect square, so both √2 and √3 are irrational, although the question mainly asks about their order.
Frequently asked questions
What is the correct answer to this question?
√2 < √3
Why is this the correct answer?
The governing concept is that the square-root function is increasing for non-negative numbers. Because 2 < 3, taking their principal square roots preserves the inequality, giving √2 < √3. This can also be checked by approximation: √2 is about 1.414 and √3 is about 1.732. Therefore option C is correct. The two numbers cannot be equal because equal non-negative square roots would have equal squares, whereas 2 and 3 are different. Option A reverses the valid inequality. Option D is also false because neither 2 nor 3 is a perfect square, so both √2 and √3 are irrational, although the question mainly asks about their order.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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