Simplify the Radical Expression square root of 72- square root of 50+3 square root of 8

$\sqrt{72} - \sqrt{50} + 3 \sqrt{8}$

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

$\sqrt{36 (2)} - \sqrt{50} + 3 \sqrt{8}$

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

$\sqrt{6^{2} \cdot 2} - \sqrt{50} + 3 \sqrt{8}$

Pull terms out from under the radical.

$| 6 | \sqrt{2} - \sqrt{50} + 3 \sqrt{8}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$6 \sqrt{2} - \sqrt{50} + 3 \sqrt{8}$

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

Factor $25$ out of $50$ .

$6 \sqrt{2} - \sqrt{25 (2)} + 3 \sqrt{8}$

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

$6 \sqrt{2} - \sqrt{5^{2} \cdot 2} + 3 \sqrt{8}$

Pull terms out from under the radical.

$6 \sqrt{2} - (| 5 | \sqrt{2}) + 3 \sqrt{8}$

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

$6 \sqrt{2} - (5 \sqrt{2}) + 3 \sqrt{8}$

Multiply $5$ by $- 1$ .

$6 \sqrt{2} - 5 \sqrt{2} + 3 \sqrt{8}$

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

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

$6 \sqrt{2} - 5 \sqrt{2} + 3 (| 2 | \sqrt{2})$

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

$6 \sqrt{2} - 5 \sqrt{2} + 3 (2 \sqrt{2})$

Multiply $2$ by $3$ .

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

Step 2

Subtract $5 \sqrt{2}$ from $6 \sqrt{2}$ .

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

Step 3

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

$7 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$

Simplify the Radical Expression square root of 72- square root of 50+3 square root of 8

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