Question

What is the simplified version of 3\sqrt{135}

Answer 1

Answer:

The simplified version of $\sqrt[3]{135}$ is $3\sqrt[3]{5}$.

Step-by-step explanation:

The given expression is

$\sqrt[3]{135}$

According to the property of radical expression.

$\sqrt[n]{x}=(x)^{\frac{1}{n}}$

Using this property we get

$\sqrt[3]{135}=(135)^{\frac{1}{3}}$

$\sqrt[3]{135}=(27\times 5)^{\frac{1}{3}}$

$\sqrt[3]{135}=(3^3\times 5)^{\frac{1}{3}}$

$\sqrt[3]{135}=(3^3)^{\frac{1}{3}}\times (5)^{\frac{1}{3}}$      $[\because (ab)^x=a^xb^x]$

$\sqrt[3]{135}=3\times \sqrt[3]{5}$     $[\because \sqrt[n]{x}=(x)^{\frac{1}{n}}]$

$\sqrt[3]{135}=3\sqrt[3]{5}$

Therefore the simplified version of $\sqrt[3]{135}$ is $3\sqrt[3]{5}$.

Answer 2

$9 \sqrt{15}$