Simplify (3 square root of 5i)/( square root of 3i)

$\frac{3 \sqrt{5} i}{\sqrt{3} i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{3 \sqrt{5} i}{\sqrt{3} i}$

Rewrite the expression.

$\frac{3 \sqrt{5}}{\sqrt{3}}$

Multiply $\frac{3 \sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{3 \sqrt{5}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Multiply $\frac{3 \sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{3 \sqrt{5} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{3 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{3 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$\frac{3 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{2}}$

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{3 \sqrt{5} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

$\frac{3 \sqrt{5} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$\frac{3 \sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{3 \sqrt{5} \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$\frac{3 \sqrt{5} \sqrt{3}}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \sqrt{5} \sqrt{3}}{3}$

Divide $\sqrt{5} \sqrt{3}$ by $1$ .

$\sqrt{5} \sqrt{3}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 3}$

Multiply $5$ by $3$ .

$\sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{15}$

Decimal Form:

$3.87298334 \dots$

Simplify (3 square root of 5i)/( square root of 3i)

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