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Simplify 9 square root of 20+2 square root of 45

$9 \sqrt{20} + 2 \sqrt{45}$

Step 1

Simplify each term.

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$9 \sqrt{4 (5)} + 2 \sqrt{45}$

Rewrite $4$ as $2^{2}$ .

$9 \sqrt{2^{2} \cdot 5} + 2 \sqrt{45}$

$9 \sqrt{2^{2} \cdot 5} + 2 \sqrt{45}$

Pull terms out from under the radical.

$9 (2 \sqrt{5}) + 2 \sqrt{45}$

Multiply $2$ by $9$ .

$18 \sqrt{5} + 2 \sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$18 \sqrt{5} + 2 \sqrt{9 (5)}$

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

$18 \sqrt{5} + 2 \sqrt{3^{2} \cdot 5}$

$18 \sqrt{5} + 2 \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$18 \sqrt{5} + 2 (3 \sqrt{5})$

Multiply $3$ by $2$ .

$18 \sqrt{5} + 6 \sqrt{5}$

$18 \sqrt{5} + 6 \sqrt{5}$

Step 2

Add $18 \sqrt{5}$ and $6 \sqrt{5}$ .

$24 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$24 \sqrt{5}$

Decimal Form:

$53.66563145 \dots$

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