Choose the correct statement relating the two expressions. A) $\sqrt { 7 } - \sqrt { 5 } \geq \sqrt { 7 - 5 }$ B) $\sqrt { 7 } - \sqrt { 5 } = \sqrt { 7 - 5 }$ C) $\sqrt { 7 } - \sqrt { 5 } \sqrt { 7 - 5 }$

Question

Choose the correct statement relating the two expressions.
A) $\sqrt { 7 } - \sqrt { 5 } \geq \sqrt { 7 - 5 }$
B) $\sqrt { 7 } - \sqrt { 5 } = \sqrt { 7 - 5 }$
C) $\sqrt { 7 } - \sqrt { 5 } < \sqrt { 7 - 5 }$
D) $\sqrt { 7 } - \sqrt { 5 } > \sqrt { 7 - 5 }$

Quizplus · Accepted Answer

The square root function is concave, meaning that for any two positive numbers $a$ and $b$, $\sqrt{a} - \sqrt{b} < \sqrt{a-b}$ if $a > b$. This is because the difference between the square roots is less than the square root of the difference.

Choose the Correct Statement Relating the Two Expressions 7−5≥7−5\sqrt { 7 } - \sqrt { 5 } \geq \sqrt { 7 - 5 }7​−5​≥7−5​

Choose the Correct Statement Relating the Two Expressions $\sqrt { 7 } - \sqrt { 5 } \geq \sqrt { 7 - 5 }$