Basic Math Examples

$\sqrt{5} m = \sqrt{7}$

Step 1

Divide each term in $\sqrt{5} m = \sqrt{7}$ by $\sqrt{5}$ .

$\frac{\sqrt{5} m}{\sqrt{5}} = \frac{\sqrt{7}}{\sqrt{5}}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\sqrt{5}$ .

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Step 2.1.1

Cancel the common factor.

$\frac{\sqrt{5} m}{\sqrt{5}} = \frac{\sqrt{7}}{\sqrt{5}}$

Step 2.1.2

Divide $m$ by $1$ .

$m = \frac{\sqrt{7}}{\sqrt{5}}$

Step 3

Simplify the right side.

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Step 3.1

Multiply $\frac{\sqrt{7}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$m = \frac{\sqrt{7}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 3.2

Combine and simplify the denominator.

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Step 3.2.1

Multiply $\frac{\sqrt{7}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$m = \frac{\sqrt{7} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Step 3.2.2

Raise $\sqrt{5}$ to the power of $1$ .

$m = \frac{\sqrt{7} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Step 3.2.3

Raise $\sqrt{5}$ to the power of $1$ .

$m = \frac{\sqrt{7} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Step 3.2.4

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

$m = \frac{\sqrt{7} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Step 3.2.5

Add $1$ and $1$ .

$m = \frac{\sqrt{7} \sqrt{5}}{{\sqrt{5}}^{2}}$

Step 3.2.6

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 3.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$m = \frac{\sqrt{7} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

Step 3.2.6.2

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

$m = \frac{\sqrt{7} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Step 3.2.6.3

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

$m = \frac{\sqrt{7} \sqrt{5}}{5^{\frac{2}{2}}}$

Step 3.2.6.4

Cancel the common factor of $2$ .

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Step 3.2.6.4.1

Cancel the common factor.

$m = \frac{\sqrt{7} \sqrt{5}}{5^{\frac{2}{2}}}$

Step 3.2.6.4.2

Rewrite the expression.

$m = \frac{\sqrt{7} \sqrt{5}}{5^{1}}$

Step 3.2.6.5

Evaluate the exponent.

$m = \frac{\sqrt{7} \sqrt{5}}{5}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Combine using the product rule for radicals.

$m = \frac{\sqrt{7 \cdot 5}}{5}$

Step 3.3.2

Multiply $7$ by $5$ .

$m = \frac{\sqrt{35}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = \frac{\sqrt{35}}{5}$

Decimal Form:

$m = 1.18321595 \dots$