# How do you simplify the square root of 18 minus the square root of 50?

Jul 25, 2015

You check to see what you can extract from those radicals.

#### Explanation:

You expression looks like this

$\sqrt{18} - \sqrt{50}$

Write the prime factors of these two numbers to see if you can find write tham as products of a perfect square and another number

$18 = 2 \cdot 9 = 2 \cdot 3 \cdot 3 = 2 \cdot {3}^{2}$

$50 = 2 \cdot 25 = 2 \cdot 5 \cdot 5 = 2 \cdot {5}^{2}$

You can thus write, with the help of the product property of radicals, an equivalent expression that looks like this

$\sqrt{2 \cdot {3}^{2}} - \sqrt{2 \cdot {5}^{2}} = \sqrt{2} \cdot \sqrt{{3}^{2}} - \sqrt{2} \cdot \sqrt{{5}^{2}}$

Finally, you get

$3 \cdot \sqrt{2} - 5 \cdot \sqrt{2} = \textcolor{g r e e n}{- 2 \sqrt{2}}$