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Simplify ( square root of 3)/2*( square root of 3)/2

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

Step 1

Multiply

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

Multiply

$\frac{\sqrt{3}}{2}$ by

$\frac{\sqrt{3}}{2}$ .

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

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add

$1$ and

$1$ .

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

Multiply

$2$ by

$2$ .

$\frac{{\sqrt{3}}^{2}}{4}$

$\frac{{\sqrt{3}}^{2}}{4}$

Step 2

Rewrite

${\sqrt{3}}^{2}$ as

$3$ .

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{3}$ as

$3^{\frac{1}{2}}$ .

$\frac{{(3^{\frac{1}{2}})}^{2}}{4}$

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{\frac{1}{2} \cdot 2}}{4}$

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{3^{\frac{2}{2}}}{4}$

Cancel the common factor of

$2$ .

Cancel the common factor.

$\frac{3^{\frac{2}{2}}}{4}$

Rewrite the expression.

$\frac{3^{1}}{4}$

$\frac{3^{1}}{4}$

Evaluate the exponent.

$\frac{3}{4}$

$\frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$

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