Evaluate 7 square root of 18+2 square root of 50

$7 \sqrt{18} + 2 \sqrt{50}$

Step 1

Simplify each term.

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

Factor $9$ out of $18$ .

$7 \sqrt{9 (2)} + 2 \sqrt{50}$

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

$7 \sqrt{3^{2} \cdot 2} + 2 \sqrt{50}$

$7 \sqrt{3^{2} \cdot 2} + 2 \sqrt{50}$

Pull terms out from under the radical.

$7 (3 \sqrt{2}) + 2 \sqrt{50}$

Multiply $3$ by $7$ .

$21 \sqrt{2} + 2 \sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$21 \sqrt{2} + 2 \sqrt{25 (2)}$

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

$21 \sqrt{2} + 2 \sqrt{5^{2} \cdot 2}$

$21 \sqrt{2} + 2 \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$21 \sqrt{2} + 2 (5 \sqrt{2})$

Multiply $5$ by $2$ .

$21 \sqrt{2} + 10 \sqrt{2}$

$21 \sqrt{2} + 10 \sqrt{2}$

Step 2

Add $21 \sqrt{2}$ and $10 \sqrt{2}$ .

$31 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$31 \sqrt{2}$

Decimal Form:

$43.84062043 \dots$

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