Evaluate square root of 72+ square root of 32+ square root of 18

$\sqrt{72} + \sqrt{32} + \sqrt{18}$

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

$\sqrt{36 (2)} + \sqrt{32} + \sqrt{18}$

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

$\sqrt{6^{2} \cdot 2} + \sqrt{32} + \sqrt{18}$

$\sqrt{6^{2} \cdot 2} + \sqrt{32} + \sqrt{18}$

Pull terms out from under the radical.

$6 \sqrt{2} + \sqrt{32} + \sqrt{18}$

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

Factor $16$ out of $32$ .

$6 \sqrt{2} + \sqrt{16 (2)} + \sqrt{18}$

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

$6 \sqrt{2} + \sqrt{4^{2} \cdot 2} + \sqrt{18}$

$6 \sqrt{2} + \sqrt{4^{2} \cdot 2} + \sqrt{18}$

Pull terms out from under the radical.

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{18}$

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

Factor $9$ out of $18$ .

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{9 (2)}$

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

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{3^{2} \cdot 2}$

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{2} + 4 \sqrt{2} + 3 \sqrt{2}$

$6 \sqrt{2} + 4 \sqrt{2} + 3 \sqrt{2}$

Step 2

Simplify by adding terms.

Add $6 \sqrt{2}$ and $4 \sqrt{2}$ .

$10 \sqrt{2} + 3 \sqrt{2}$

Add $10 \sqrt{2}$ and $3 \sqrt{2}$ .

$13 \sqrt{2}$

$13 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{2}$

Decimal Form:

$18.38477631 \dots$

Related Questions