Simplify the Radical Expression (8 square root of 5)/(4 square root of 3)

$\frac{8 \sqrt{5}}{4 \sqrt{3}}$

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 \sqrt{5}$ .

$\frac{4 (2 \sqrt{5})}{4 \sqrt{3}}$

Cancel the common factors.

Factor $4$ out of $4 \sqrt{3}$ .

$\frac{4 (2 \sqrt{5})}{4 (\sqrt{3})}$

Cancel the common factor.

$\frac{4 (2 \sqrt{5})}{4 \sqrt{3}}$

Rewrite the expression.

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

Multiply $\frac{2 \sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $3$ by $5$ .

$\frac{2 \sqrt{15}}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{15}}{3}$

Decimal Form:

$2.58198889 \dots$

Simplify the Radical Expression (8 square root of 5)/(4 square root of 3)

Related Questions

Support LCMGCF.com by disabling your adblocker.