Simplify the Radical Expression square root of 8+ square root of 18+ square root of 50- square root of 32

$\sqrt{8} + \sqrt{18} + \sqrt{50} - \sqrt{32}$

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{4 (2)} + \sqrt{18} + \sqrt{50} - \sqrt{32}$

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

$\sqrt{2^{2} \cdot 2} + \sqrt{18} + \sqrt{50} - \sqrt{32}$

Pull terms out from under the radical.

$| 2 | \sqrt{2} + \sqrt{18} + \sqrt{50} - \sqrt{32}$

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

$2 \sqrt{2} + \sqrt{18} + \sqrt{50} - \sqrt{32}$

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

Factor $9$ out of $18$ .

$2 \sqrt{2} + \sqrt{9 (2)} + \sqrt{50} - \sqrt{32}$

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

$2 \sqrt{2} + \sqrt{3^{2} \cdot 2} + \sqrt{50} - \sqrt{32}$

Pull terms out from under the radical.

$2 \sqrt{2} + | 3 | \sqrt{2} + \sqrt{50} - \sqrt{32}$

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

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{50} - \sqrt{32}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{25 (2)} - \sqrt{32}$

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

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{5^{2} \cdot 2} - \sqrt{32}$

Pull terms out from under the radical.

$2 \sqrt{2} + 3 \sqrt{2} + | 5 | \sqrt{2} - \sqrt{32}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$2 \sqrt{2} + 3 \sqrt{2} + 5 \sqrt{2} - \sqrt{32}$

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

Factor $16$ out of $32$ .

$2 \sqrt{2} + 3 \sqrt{2} + 5 \sqrt{2} - \sqrt{16 (2)}$

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

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

Pull terms out from under the radical.

$2 \sqrt{2} + 3 \sqrt{2} + 5 \sqrt{2} - (| 4 | \sqrt{2})$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$2 \sqrt{2} + 3 \sqrt{2} + 5 \sqrt{2} - (4 \sqrt{2})$

Multiply $4$ by $- 1$ .

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

Step 2

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

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

Step 3

Add $5 \sqrt{2}$ and $5 \sqrt{2}$ .

$10 \sqrt{2} - 4 \sqrt{2}$

Step 4

Subtract $4 \sqrt{2}$ from $10 \sqrt{2}$ .

$6 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$

Simplify the Radical Expression square root of 8+ square root of 18+ square root of 50- square root of 32

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