Simplify (8- square root of 18)/( square root of 2)

$\frac{8 - \sqrt{18}}{\sqrt{2}}$

Step 1

Simplify the numerator.

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

Factor $9$ out of $18$ .

$\frac{8 - \sqrt{9 (2)}}{\sqrt{2}}$

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

$\frac{8 - \sqrt{3^{2} \cdot 2}}{\sqrt{2}}$

Pull terms out from under the radical.

$\frac{8 - (3 \sqrt{2})}{\sqrt{2}}$

Multiply $3$ by $- 1$ .

$\frac{8 - 3 \sqrt{2}}{\sqrt{2}}$

Step 2

Multiply $\frac{8 - 3 \sqrt{2}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{8 - 3 \sqrt{2}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{8 - 3 \sqrt{2}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{{\sqrt{2}}^{2}}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{2^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{2^{1}}$

Evaluate the exponent.

$\frac{(8 - 3 \sqrt{2}) \sqrt{2}}{2}$

Step 4

Apply the distributive property.

$\frac{8 \sqrt{2} - 3 \sqrt{2} \sqrt{2}}{2}$

Step 5

Multiply $- 3 \sqrt{2} \sqrt{2}$ .

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{8 \sqrt{2} - 3 ({\sqrt{2}}^{1} \sqrt{2})}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{8 \sqrt{2} - 3 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 \sqrt{2} - 3 {\sqrt{2}}^{1 + 1}}{2}$

Add $1$ and $1$ .

$\frac{8 \sqrt{2} - 3 {\sqrt{2}}^{2}}{2}$

Step 6

Simplify each term.

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{8 \sqrt{2} - 3 {(2^{\frac{1}{2}})}^{2}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{8 \sqrt{2} - 3 \cdot 2^{\frac{1}{2} \cdot 2}}{2}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{8 \sqrt{2} - 3 \cdot 2^{\frac{2}{2}}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{8 \sqrt{2} - 3 \cdot 2^{\frac{2}{2}}}{2}$

Rewrite the expression.

$\frac{8 \sqrt{2} - 3 \cdot 2^{1}}{2}$

Evaluate the exponent.

$\frac{8 \sqrt{2} - 3 \cdot 2}{2}$

Multiply $- 3$ by $2$ .

$\frac{8 \sqrt{2} - 6}{2}$

Step 7

Cancel the common factor of $8 \sqrt{2} - 6$ and $2$ .

Factor $2$ out of $8 \sqrt{2}$ .

$\frac{2 (4 \sqrt{2}) - 6}{2}$

Factor $2$ out of $- 6$ .

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

Factor $2$ out of $2 (4 \sqrt{2}) + 2 (- 3)$ .

$\frac{2 (4 \sqrt{2} - 3)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (4 \sqrt{2} - 3)}{2 (1)}$

Cancel the common factor.

$\frac{2 (4 \sqrt{2} - 3)}{2 \cdot 1}$

Rewrite the expression.

$\frac{4 \sqrt{2} - 3}{1}$

Divide $4 \sqrt{2} - 3$ by $1$ .

$4 \sqrt{2} - 3$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2} - 3$

Decimal Form:

$2.65685424 \dots$

Simplify (8- square root of 18)/( square root of 2)

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