Basic Math Examples

$\frac{1}{2} \cdot (1.5 \cdot 0.6 + \frac{1.3}{\sqrt{0.52}})$

Step 1

Simplify each term.

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Step 1.1

Multiply $1.5$ by $0.6$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3}{\sqrt{0.52}})$

Step 1.2

Multiply $\frac{1.3}{\sqrt{0.52}}$ by $\frac{\sqrt{0.52}}{\sqrt{0.52}}$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3}{\sqrt{0.52}} \cdot \frac{\sqrt{0.52}}{\sqrt{0.52}})$

Step 1.3

Combine and simplify the denominator.

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Step 1.3.1

Multiply $\frac{1.3}{\sqrt{0.52}}$ by $\frac{\sqrt{0.52}}{\sqrt{0.52}}$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{\sqrt{0.52} \sqrt{0.52}})$

Step 1.3.2

Raise $\sqrt{0.52}$ to the power of $1$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{\sqrt{0.52}}^{1} \sqrt{0.52}})$

Step 1.3.3

Raise $\sqrt{0.52}$ to the power of $1$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{\sqrt{0.52}}^{1} {\sqrt{0.52}}^{1}})$

Step 1.3.4

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

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{\sqrt{0.52}}^{1 + 1}})$

Step 1.3.5

Add $1$ and $1$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{\sqrt{0.52}}^{2}})$

Step 1.3.6

Rewrite ${\sqrt{0.52}}^{2}$ as $0.52$ .

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Step 1.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.52}$ as ${0.52}^{\frac{1}{2}}$ .

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{({0.52}^{\frac{1}{2}})}^{2}})$

Step 1.3.6.2

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

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{0.52}^{\frac{1}{2} \cdot 2}})$

Step 1.3.6.3

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

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{0.52}^{\frac{2}{2}}})$

Step 1.3.6.4

Cancel the common factor of $2$ .

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Step 1.3.6.4.1

Cancel the common factor.

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{0.52}^{\frac{2}{2}}})$

Step 1.3.6.4.2

Rewrite the expression.

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{{0.52}^{1}})$

Step 1.3.6.5

Evaluate the exponent.

$\frac{1}{2} \cdot (0.9 + \frac{1.3 \sqrt{0.52}}{0.52})$

Step 1.4

Multiply $1.3$ by $\sqrt{0.52}$ .

$\frac{1}{2} \cdot (0.9 + \frac{0.93744333}{0.52})$

Step 1.5

Divide $0.93744333$ by $0.52$ .

$\frac{1}{2} \cdot (0.9 + 1.80277563)$

Step 2

Combine fractions.

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Step 2.1

Add $0.9$ and $1.80277563$ .

$\frac{1}{2} \cdot 2.70277563$

Step 2.2

Combine $\frac{1}{2}$ and $2.70277563$ .

$\frac{2.70277563}{2}$

Step 2.3

Divide $2.70277563$ by $2$ .

$1.35138781$