Algebra Examples

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

Step 1

Subtract $\sqrt{\frac{m}{10}}$ from both sides of the equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

Combine and simplify the denominator.

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Step 2.1.3.1

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

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

Step 2.1.3.2

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

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

Step 2.1.3.3

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

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

Step 2.1.3.4

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

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

Step 2.1.3.5

Add $1$ and $1$ .

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

Step 2.1.3.6

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

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Step 2.1.3.6.1

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

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

Step 2.1.3.6.2

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

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

Step 2.1.3.6.3

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

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

Step 2.1.3.6.4

Cancel the common factor of $2$ .

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Step 2.1.3.6.4.1

Cancel the common factor.

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

Step 2.1.3.6.4.2

Rewrite the expression.

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

Step 2.1.3.6.5

Evaluate the exponent.

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

Step 2.1.4

Combine using the product rule for radicals.

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

Step 2.2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Multiply $10$ by $10$ .

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

Step 7

Set the numerator equal to zero.

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

Step 8

Solve the equation for $m$ .

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Step 8.1

Subtract $100$ from both sides of the equation.

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

Step 8.2

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

${(- \sqrt{10 m})}^{2} = {(- 100)}^{2}$

Step 8.3

Simplify each side of the equation.

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Step 8.3.1

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

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

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Simplify ${(- {(10 m)}^{\frac{1}{2}})}^{2}$ .

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Step 8.3.2.1.1

Apply the product rule to $10 m$ .

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

Step 8.3.2.1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 8.3.2.1.2.1

Apply the product rule to $- 10^{\frac{1}{2}} m^{\frac{1}{2}}$ .

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

Step 8.3.2.1.2.2

Apply the product rule to $- 10^{\frac{1}{2}}$ .

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

Step 8.3.2.1.3

Raise $- 1$ to the power of $2$ .

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

Step 8.3.2.1.4

Multiply ${(10^{\frac{1}{2}})}^{2}$ by $1$ .

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

Step 8.3.2.1.5

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

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Step 8.3.2.1.5.1

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

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

Step 8.3.2.1.5.2

Cancel the common factor of $2$ .

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Step 8.3.2.1.5.2.1

Cancel the common factor.

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

Step 8.3.2.1.5.2.2

Rewrite the expression.

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

Step 8.3.2.1.6

Evaluate the exponent.

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

Step 8.3.2.1.7

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

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Step 8.3.2.1.7.1

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

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

Step 8.3.2.1.7.2

Cancel the common factor of $2$ .

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Step 8.3.2.1.7.2.1

Cancel the common factor.

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

Step 8.3.2.1.7.2.2

Rewrite the expression.

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

Step 8.3.2.1.8

Simplify.

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

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

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

$10 m = 10000$

Step 8.4

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

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Step 8.4.1

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

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

Step 8.4.2

Simplify the left side.

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Step 8.4.2.1

Cancel the common factor of $10$ .

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Step 8.4.2.1.1

Cancel the common factor.

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

Step 8.4.2.1.2

Divide $m$ by $1$ .

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

Step 8.4.3

Simplify the right side.

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Step 8.4.3.1

Divide $10000$ by $10$ .

$m = 1000$