Evaluate 5 square root of 18+4 square root of 32

$5 \sqrt{18} + 4 \sqrt{32}$

Step 1

Simplify each term.

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

Factor $9$ out of $18$ .

$5 \sqrt{9 (2)} + 4 \sqrt{32}$

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

$5 \sqrt{3^{2} \cdot 2} + 4 \sqrt{32}$

$5 \sqrt{3^{2} \cdot 2} + 4 \sqrt{32}$

Pull terms out from under the radical.

$5 (3 \sqrt{2}) + 4 \sqrt{32}$

Multiply $3$ by $5$ .

$15 \sqrt{2} + 4 \sqrt{32}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$15 \sqrt{2} + 4 \sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$15 \sqrt{2} + 4 \sqrt{4^{2} \cdot 2}$

$15 \sqrt{2} + 4 \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$15 \sqrt{2} + 4 (4 \sqrt{2})$

Multiply $4$ by $4$ .

$15 \sqrt{2} + 16 \sqrt{2}$

$15 \sqrt{2} + 16 \sqrt{2}$

Step 2

Add $15 \sqrt{2}$ and $16 \sqrt{2}$ .

$31 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$31 \sqrt{2}$

Decimal Form:

$43.84062043 \dots$

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