Evaluate square root of 32+ square root of 98

$\sqrt{32} + \sqrt{98}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$\sqrt{16 (2)} + \sqrt{98}$

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

$\sqrt{4^{2} \cdot 2} + \sqrt{98}$

$\sqrt{4^{2} \cdot 2} + \sqrt{98}$

Pull terms out from under the radical.

$4 \sqrt{2} + \sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$4 \sqrt{2} + \sqrt{49 (2)}$

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

$4 \sqrt{2} + \sqrt{7^{2} \cdot 2}$

$4 \sqrt{2} + \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt{2} + 7 \sqrt{2}$

$4 \sqrt{2} + 7 \sqrt{2}$

Step 2

Add $4 \sqrt{2}$ and $7 \sqrt{2}$ .

$11 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$11 \sqrt{2}$

Decimal Form:

$15.55634918 \dots$

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