Simplify the Radical Expression - square root of 6+ square root of 150

$- \sqrt{6} + \sqrt{150}$

Step 1

Simplify each term.

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$- \sqrt{6} + \sqrt{25 (6)}$

Rewrite $25$ as $5^{2}$ .

$- \sqrt{6} + \sqrt{5^{2} \cdot 6}$

Pull terms out from under the radical.

$- \sqrt{6} + | 5 | \sqrt{6}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$- \sqrt{6} + 5 \sqrt{6}$

Step 2

Add $- \sqrt{6}$ and $5 \sqrt{6}$ .

$4 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{6}$

Decimal Form:

$9.79795897 \dots$