Solve for x 8=x square root of 2

$8 = x \sqrt{2}$

Step 1

Rewrite the equation as $x \sqrt{2} = 8$ .

$x \sqrt{2} = 8$

Step 2

Divide each term in $x \sqrt{2} = 8$ by $\sqrt{2}$ and simplify.

Divide each term in $x \sqrt{2} = 8$ by $\sqrt{2}$ .

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{8}{\sqrt{2}}$

Simplify the left side.

Cancel the common factor of $\sqrt{2}$ .

Cancel the common factor.

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{8}{\sqrt{2}}$

Divide $x$ by $1$ .

$x = \frac{8}{\sqrt{2}}$

Simplify the right side.

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

$x = \frac{8}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Combine and simplify the denominator.

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

$x = \frac{8 \sqrt{2}}{\sqrt{2} \sqrt{2}}$

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

$x = \frac{8 \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

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

$x = \frac{8 \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

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

$x = \frac{8 \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$x = \frac{8 \sqrt{2}}{{\sqrt{2}}^{2}}$

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

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

$x = \frac{8 \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

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

$x = \frac{8 \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

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

$x = \frac{8 \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \frac{8 \sqrt{2}}{2^{\frac{2}{2}}}$

Rewrite the expression.

$x = \frac{8 \sqrt{2}}{2^{1}}$

Evaluate the exponent.

$x = \frac{8 \sqrt{2}}{2}$

Cancel the common factor of $8$ and $2$ .

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

$x = \frac{2 (4 \sqrt{2})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (4 \sqrt{2})}{2 (1)}$

Cancel the common factor.

$x = \frac{2 (4 \sqrt{2})}{2 \cdot 1}$

Rewrite the expression.

$x = \frac{4 \sqrt{2}}{1}$

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

$x = 4 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt{2}$

Decimal Form:

$x = 5.65685424 \dots$

Solve for x 8=x square root of 2

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