Question

Let \(a\) and \(b\) be two real numbers with \(a,b > 0\) and \(a < b\). Then which of the following is true?

• A. $\sqrt{a} < \sqrt{b}$
• B. $\sqrt{b} < \sqrt{a}$
• C. $\text{b}^2 < \text{a}^2$
• D. $\text{a}^2 - \text{b}^2 > 0$

Hint:

For positive numbers, operations like squaring, cubing, or taking the square root always preserve the direction of the inequality, whereas taking the reciprocal reverses it (i.e., \( a \frac{1}{b} \)).

Answer 1

The Correct Option is A