Precalculus Examples

$\frac{\frac{3}{2}}{\sqrt{4 - 2.25}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{2} \cdot \frac{1}{\sqrt{4 - 2.25}}$

Step 2

Subtract $2.25$ from $4$ .

$\frac{3}{2} \cdot \frac{1}{\sqrt{1.75}}$

Step 3

Multiply $\frac{1}{\sqrt{1.75}}$ by $\frac{\sqrt{1.75}}{\sqrt{1.75}}$ .

$\frac{3}{2} (\frac{1}{\sqrt{1.75}} \cdot \frac{\sqrt{1.75}}{\sqrt{1.75}})$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{1}{\sqrt{1.75}}$ by $\frac{\sqrt{1.75}}{\sqrt{1.75}}$ .

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{\sqrt{1.75} \sqrt{1.75}}$

Step 4.2

Raise $\sqrt{1.75}$ to the power of $1$ .

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{\sqrt{1.75}}^{1} \sqrt{1.75}}$

Step 4.3

Raise $\sqrt{1.75}$ to the power of $1$ .

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{\sqrt{1.75}}^{1} {\sqrt{1.75}}^{1}}$

Step 4.4

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

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{\sqrt{1.75}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{\sqrt{1.75}}^{2}}$

Step 4.6

Rewrite ${\sqrt{1.75}}^{2}$ as $1.75$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{1.75}$ as ${1.75}^{\frac{1}{2}}$ .

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{({1.75}^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{1.75}^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{1.75}^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{1.75}^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{{1.75}^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{3}{2} \cdot \frac{\sqrt{1.75}}{1.75}$

Step 5

Evaluate the root.

$\frac{3}{2} \cdot \frac{1.32287565}{1.75}$

Step 6

Divide $1.32287565$ by $1.75$ .

$\frac{3}{2} \cdot 0.75592894$

Step 7

Multiply $\frac{3}{2} \cdot 0.75592894$ .

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Step 7.1

Combine $\frac{3}{2}$ and $0.75592894$ .

$\frac{3 \cdot 0.75592894}{2}$

Step 7.2

Multiply $3$ by $0.75592894$ .

$\frac{2.26778683}{2}$

Step 8

Divide $2.26778683$ by $2$ .

$1.13389341$