Basic Math Examples

$\frac{0.29 - 0.25}{\sqrt{\frac{(0.25) (0.75)}{510}}}$

Step 1

Multiply $0.25$ by $0.75$ .

$\frac{0.29 - 0.25}{\sqrt{\frac{0.1875}{510}}}$

Step 2

Subtract $0.25$ from $0.29$ .

$\frac{0.04}{\sqrt{\frac{0.1875}{510}}}$

Step 3

Divide $0.1875$ by $510$ .

$\frac{0.04}{\sqrt{0.00036764}}$

Step 4

Multiply $\frac{0.04}{\sqrt{0.00036764}}$ by $\frac{\sqrt{0.00036764}}{\sqrt{0.00036764}}$ .

$\frac{0.04}{\sqrt{0.00036764}} \cdot \frac{\sqrt{0.00036764}}{\sqrt{0.00036764}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{0.04}{\sqrt{0.00036764}}$ by $\frac{\sqrt{0.00036764}}{\sqrt{0.00036764}}$ .

$\frac{0.04 \sqrt{0.00036764}}{\sqrt{0.00036764} \sqrt{0.00036764}}$

Step 5.2

Raise $\sqrt{0.00036764}$ to the power of $1$ .

$\frac{0.04 \sqrt{0.00036764}}{{\sqrt{0.00036764}}^{1} \sqrt{0.00036764}}$

Step 5.3

Raise $\sqrt{0.00036764}$ to the power of $1$ .

$\frac{0.04 \sqrt{0.00036764}}{{\sqrt{0.00036764}}^{1} {\sqrt{0.00036764}}^{1}}$

Step 5.4

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

$\frac{0.04 \sqrt{0.00036764}}{{\sqrt{0.00036764}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

$\frac{0.04 \sqrt{0.00036764}}{{\sqrt{0.00036764}}^{2}}$

Step 5.6

Rewrite ${\sqrt{0.00036764}}^{2}$ as $0.00036764$ .

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Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.00036764}$ as ${0.00036764}^{\frac{1}{2}}$ .

$\frac{0.04 \sqrt{0.00036764}}{{({0.00036764}^{\frac{1}{2}})}^{2}}$

Step 5.6.2

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

$\frac{0.04 \sqrt{0.00036764}}{{0.00036764}^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

$\frac{0.04 \sqrt{0.00036764}}{{0.00036764}^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$\frac{0.04 \sqrt{0.00036764}}{{0.00036764}^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$\frac{0.04 \sqrt{0.00036764}}{{0.00036764}^{1}}$

Step 5.6.5

Evaluate the exponent.

$\frac{0.04 \sqrt{0.00036764}}{0.00036764}$

Step 6

Multiply $0.04$ by $\sqrt{0.00036764}$ .

$\frac{0.00076696}{0.00036764}$

Step 7

Divide $0.00076696$ by $0.00036764$ .

$2.08614476$