Question

which expression is equal to 7\sqrt{28}-5\sqrt{63}?
-\sqrt{7}
-37\sqrt{7}
-11\sqrt{7}
\sqrt{7}

Explanation:

Step1: Simplify $\sqrt{28}$

$\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}$

Step2: Simplify $\sqrt{63}$

$\sqrt{63}=\sqrt{9\times7}=3\sqrt{7}$

Step3: Substitute into the original expression

$7\sqrt{28}-5\sqrt{63}=7\times2\sqrt{7}-5\times3\sqrt{7}=14\sqrt{7}-15\sqrt{7}$

Step4: Combine like - terms

$14\sqrt{7}-15\sqrt{7}=(14 - 15)\sqrt{7}=-\sqrt{7}$

Answer:

$-\sqrt{7}$