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Evaluate square root of 63+ square root of 343

$\sqrt{63} + \sqrt{343}$

Step 1

Simplify each term.

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$\sqrt{9 (7)} + \sqrt{343}$

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

$\sqrt{3^{2} \cdot 7} + \sqrt{343}$

$\sqrt{3^{2} \cdot 7} + \sqrt{343}$

Pull terms out from under the radical.

$3 \sqrt{7} + \sqrt{343}$

Rewrite $343$ as $7^{2} \cdot 7$ .

Factor $49$ out of $343$ .

$3 \sqrt{7} + \sqrt{49 (7)}$

Rewrite $49$ as $7^{2}$ .

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

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

Pull terms out from under the radical.

$3 \sqrt{7} + 7 \sqrt{7}$

$3 \sqrt{7} + 7 \sqrt{7}$

Step 2

Add $3 \sqrt{7}$ and $7 \sqrt{7}$ .

$10 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{7}$

Decimal Form:

$26.45751311 \dots$

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