Simplify (9 square root of 2)/( square root of 10+ square root of 18)

$\frac{9 \sqrt{2}}{\sqrt{10 + \sqrt{18}}}$

Step 1

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{9 \sqrt{2}}{\sqrt{10 + \sqrt{9 (2)}}}$

Rewrite $9$ as $3^{2}$ .

$\frac{9 \sqrt{2}}{\sqrt{10 + \sqrt{3^{2} \cdot 2}}}$

Step 2

Pull terms out from under the radical.

$\frac{9 \sqrt{2}}{\sqrt{10 + 3 \sqrt{2}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{9 \sqrt{2}}{\sqrt{10 + 3 \sqrt{2}}}$

Decimal Form:

$3.37257990 \dots$