# What is 5 the square root of 8 • 4 the square root of 7?

Sep 28, 2015

Multiply the numbers and the squares separately and and remember that $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$

#### Explanation:

$5 \cdot \sqrt{8} \cdot 4 \cdot \sqrt{7} = 5 \cdot 4 \cdot \sqrt{8} \cdot \sqrt{7} = 20 \cdot \sqrt{8 \cdot 7} = 20 \sqrt{56}$

We're not done yet, because $56 = 4 \cdot 14 = {2}^{2} \cdot 14$
and we can take the square out of the root:

$= 20 \cdot \sqrt{{2}^{2} \cdot 14} = 20 \cdot \sqrt{{2}^{2}} \cdot \sqrt{14} = 20 \cdot 2 \cdot \sqrt{14}$

Final answer: $40 \sqrt{14}$