Evaluate square root of 8+ square root of 98+ square root of 72

$\sqrt{8} + \sqrt{98} + \sqrt{72}$

Step 1

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2)} + \sqrt{98} + \sqrt{72}$

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

$\sqrt{2^{2} \cdot 2} + \sqrt{98} + \sqrt{72}$

$\sqrt{2^{2} \cdot 2} + \sqrt{98} + \sqrt{72}$

Pull terms out from under the radical.

$2 \sqrt{2} + \sqrt{98} + \sqrt{72}$

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

Factor $49$ out of $98$ .

$2 \sqrt{2} + \sqrt{49 (2)} + \sqrt{72}$

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

$2 \sqrt{2} + \sqrt{7^{2} \cdot 2} + \sqrt{72}$

$2 \sqrt{2} + \sqrt{7^{2} \cdot 2} + \sqrt{72}$

Pull terms out from under the radical.

$2 \sqrt{2} + 7 \sqrt{2} + \sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$2 \sqrt{2} + 7 \sqrt{2} + \sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$2 \sqrt{2} + 7 \sqrt{2} + \sqrt{6^{2} \cdot 2}$

$2 \sqrt{2} + 7 \sqrt{2} + \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$2 \sqrt{2} + 7 \sqrt{2} + 6 \sqrt{2}$

$2 \sqrt{2} + 7 \sqrt{2} + 6 \sqrt{2}$

Step 2

Simplify by adding terms.

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

$9 \sqrt{2} + 6 \sqrt{2}$

Add $9 \sqrt{2}$ and $6 \sqrt{2}$ .

$15 \sqrt{2}$

$15 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{2}$

Decimal Form:

$21.21320343 \dots$

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