Question

Simplify the square root of 5 times the cube root of 5.

Answer 1

Answer:

it's the third option!!!!!!!!!!!!

Answer 2

Answer:

Option 3 - five to the two thirds power

Step-by-step explanation:

Given : Expression 'the square root of 5 times the cube root of 5'.

To find : Simplify the expression ?

Solution :

Writing expression in numeric form,

The cube root of 5 means $\sqrt[3]{5}$

The square root of 5 times the cube root of 5 means $\sqrt{5\sqrt[3]{5}}$

Now, simplify the expression

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

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

$\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{\frac{4}{3}}}$

$\sqrt{5\sqrt[3]{5}}=((5)^{\frac{4}{3}})^{\frac{1}{2}}$

$\sqrt{5\sqrt[3]{5}}=(5)^{\frac{4}{3}\times \frac{1}{2}}$

$\sqrt{5\sqrt[3]{5}}=(5)^{\frac{2}{3}}$

The expression is five to the two thirds power.

Therefore, Option 3 is correct.