How do you simplify sqrt112-sqrt63?

Jul 13, 2016

$\sqrt{7}$

Explanation:

$\sqrt{112} - \sqrt{63}$

the prime factors for each square root become

$\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 7} - \sqrt{3 \cdot 3 \cdot 7}$

factor out the pairs

$2 \cdot 2 \sqrt{7} - 3 \sqrt{7}$

$4 \sqrt{7} - 3 \sqrt{7}$

$\sqrt{7}$