Simplify square root of 32- square root of 18+ square root of 54+ square root of 150

$\sqrt{32} - \sqrt{18} + \sqrt{54} + \sqrt{150}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$\sqrt{16 (2)} - \sqrt{18} + \sqrt{54} + \sqrt{150}$

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

$\sqrt{4^{2} \cdot 2} - \sqrt{18} + \sqrt{54} + \sqrt{150}$

Pull terms out from under the radical.

$4 \sqrt{2} - \sqrt{18} + \sqrt{54} + \sqrt{150}$

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

Factor $9$ out of $18$ .

$4 \sqrt{2} - \sqrt{9 (2)} + \sqrt{54} + \sqrt{150}$

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

$4 \sqrt{2} - \sqrt{3^{2} \cdot 2} + \sqrt{54} + \sqrt{150}$

Pull terms out from under the radical.

$4 \sqrt{2} - (3 \sqrt{2}) + \sqrt{54} + \sqrt{150}$

Multiply $3$ by $- 1$ .

$4 \sqrt{2} - 3 \sqrt{2} + \sqrt{54} + \sqrt{150}$

Rewrite $54$ as $3^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$4 \sqrt{2} - 3 \sqrt{2} + \sqrt{9 (6)} + \sqrt{150}$

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

$4 \sqrt{2} - 3 \sqrt{2} + \sqrt{3^{2} \cdot 6} + \sqrt{150}$

Pull terms out from under the radical.

$4 \sqrt{2} - 3 \sqrt{2} + 3 \sqrt{6} + \sqrt{150}$

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$4 \sqrt{2} - 3 \sqrt{2} + 3 \sqrt{6} + \sqrt{25 (6)}$

Rewrite $25$ as $5^{2}$ .

$4 \sqrt{2} - 3 \sqrt{2} + 3 \sqrt{6} + \sqrt{5^{2} \cdot 6}$

Pull terms out from under the radical.

$4 \sqrt{2} - 3 \sqrt{2} + 3 \sqrt{6} + 5 \sqrt{6}$

Step 2

Simplify by adding terms.

Subtract $3 \sqrt{2}$ from $4 \sqrt{2}$ .

$\sqrt{2} + 3 \sqrt{6} + 5 \sqrt{6}$

Add $3 \sqrt{6}$ and $5 \sqrt{6}$ .

$\sqrt{2} + 8 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2} + 8 \sqrt{6}$

Decimal Form:

$21.01013150 \dots$