Solve by Factoring 10 = square root of m/10

$10 = \sqrt{\frac{m}{10}}$

Move $\sqrt{\frac{m}{10}}$ to the left side of the equation by subtracting it from both sides.

$10 - \sqrt{\frac{m}{10}} = 0$

Simplify $10 - \sqrt{\frac{m}{10}}$ .

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Simplify each term.

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Rewrite $\sqrt{\frac{m}{10}}$ as $\frac{\sqrt{m}}{\sqrt{10}}$ .

$10 - \frac{\sqrt{m}}{\sqrt{10}} = 0$

Multiply $\frac{\sqrt{m}}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$10 - (\frac{\sqrt{m}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}) = 0$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{m}}{\sqrt{10}}$ and $\frac{\sqrt{10}}{\sqrt{10}}$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{\sqrt{10} \sqrt{10}} = 0$

Raise $\sqrt{10}$ to the power of $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}} = 0$

Raise $\sqrt{10}$ to the power of $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}} = 0$

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

$10 - \frac{\sqrt{m} \sqrt{10}}{{\sqrt{10}}^{1 + 1}} = 0$

Add $1$ and $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{{\sqrt{10}}^{2}} = 0$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}} = 0$

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

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{\frac{1}{2} \cdot 2}} = 0$

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

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{\frac{2}{2}}} = 0$

Cancel the common factor of $2$ .

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Cancel the common factor.

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{\frac{2}{2}}} = 0$

Divide $1$ by $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{1}} = 0$

Evaluate the exponent.

$10 - \frac{\sqrt{m} \sqrt{10}}{10} = 0$

Combine using the product rule for radicals.

$10 - \frac{\sqrt{m \cdot 10}}{10} = 0$

Reorder factors in $10 - \frac{\sqrt{m \cdot 10}}{10}$ .

$10 - \frac{\sqrt{10 m}}{10} = 0$

Simplify each term.

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Rewrite $\sqrt{\frac{m}{10}}$ as $\frac{\sqrt{m}}{\sqrt{10}}$ .

$10 - \frac{\sqrt{m}}{\sqrt{10}} = 0$

Multiply $\frac{\sqrt{m}}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$10 - (\frac{\sqrt{m}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}) = 0$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{m}}{\sqrt{10}}$ and $\frac{\sqrt{10}}{\sqrt{10}}$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{\sqrt{10} \sqrt{10}} = 0$

Raise $\sqrt{10}$ to the power of $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{\sqrt{10} \sqrt{10}} = 0$

Raise $\sqrt{10}$ to the power of $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{\sqrt{10} \sqrt{10}} = 0$

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

$10 - \frac{\sqrt{m} \sqrt{10}}{{\sqrt{10}}^{1 + 1}} = 0$

Add $1$ and $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{{\sqrt{10}}^{2}} = 0$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}} = 0$

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

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{\frac{1}{2} \cdot 2}} = 0$

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

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{\frac{2}{2}}} = 0$

Cancel the common factor of $2$ .

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Cancel the common factor.

$10 - \frac{\sqrt{m} \sqrt{10}}{10^{\frac{2}{2}}} = 0$

Divide $1$ by $1$ .

$10 - \frac{\sqrt{m} \sqrt{10}}{10} = 0$

Evaluate the exponent.

$10 - \frac{\sqrt{m} \sqrt{10}}{10} = 0$

Combine using the product rule for radicals.

$10 - \frac{\sqrt{m \cdot 10}}{10} = 0$

Reorder factors in $10 - \frac{\sqrt{m \cdot 10}}{10}$ .

$10 - \frac{\sqrt{10 m}}{10} = 0$

To write $10$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$10 \cdot \frac{10}{10} - \frac{\sqrt{10 m}}{10} = 0$

Combine $10$ and $\frac{10}{10}$ .

$\frac{10 \cdot 10}{10} - \frac{\sqrt{10 m}}{10} = 0$

Combine the numerators over the common denominator.

$\frac{10 \cdot 10 - \sqrt{10 m}}{10} = 0$

Multiply $10$ by $10$ .

$\frac{100 - \sqrt{10 m}}{10} = 0$

Multiply both sides of the equation by $10$ .

$100 - \sqrt{10 m} = 0 \cdot (10)$

Remove parentheses.

$100 - \sqrt{10 m} = 0 \cdot (10)$

Multiply $0$ by $10$ .

$100 - \sqrt{10 m} = 0$

Subtract $100$ from both sides of the equation.

$- \sqrt{10 m} = - 100$

Multiply each term in $- \sqrt{10 m} = - 100$ by $- 1$

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Multiply each term in $- \sqrt{10 m} = - 100$ by $- 1$ .

$(- \sqrt{10 m}) \cdot - 1 = (- 100) \cdot - 1$

Multiply $- \sqrt{10 m} \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 \sqrt{10 m} = (- 100) \cdot - 1$

Multiply $\sqrt{10 m}$ by $1$ .

$\sqrt{10 m} = (- 100) \cdot - 1$

Multiply $- 100$ by $- 1$ .

$\sqrt{10 m} = 100$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{10 m}}^{2} = 100^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(10 m)}^{\frac{1}{2}})}^{2}$ .

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

${(10 m)}^{\frac{1}{2} \cdot 2} = 100^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(10 m)}^{\frac{1}{2} \cdot 2} = 100^{2}$

Rewrite the expression.

${(10 m)}^{1} = 100^{2}$

Simplify.

$10 m = 100^{2}$

Raise $100$ to the power of $2$ .

$10 m = 10000$

Divide each term by $10$ and simplify.

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Divide each term in $10 m = 10000$ by $10$ .

$\frac{10 m}{10} = \frac{10000}{10}$

Cancel the common factor of $10$ .

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Cancel the common factor.

$\frac{10 m}{10} = \frac{10000}{10}$

Divide $m$ by $1$ .

$m = \frac{10000}{10}$

Divide $10000$ by $10$ .

$m = 1000$

Solve by Factoring 10 = square root of m/10

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