Simplify the Radical Expression square root of 8+ square root of 18

$\sqrt{8} + \sqrt{18}$

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{4 (2)} + \sqrt{18}$

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

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

Pull terms out from under the radical.

$| 2 | \sqrt{2} + \sqrt{18}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

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

Factor $9$ out of $18$ .

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

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

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Step 2

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

$5 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$