Question

Simplify the square root of 3 times the fifth root of 3.

three to the one tenth power
three to the three fifths power
three to the nine tenths power
three to the seven tenths power

Answer 1

Answer:

The last option:  3^(7/10).

Step-by-step explanation:

√3 *  ⁵√3

= 3^1/2 * 3*1/5

= 3^(1/2*1/5)

= 3^(7/10).

Answer 2

Answer:

Three to the three fifths power.

Step-by-step explanation:

The given expression is

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

To simplify this expression, we have to use a specific power property which allow us to transform a root into a power with a fractional exponent, the property states:

$\sqrt[n]{x^{m}}=x^{\frac{m}{n}}$

Applying the property, we have:

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

Now, we multiply exponents:

$(3(3)^{\frac{1}{5}})^{\frac{1}{2}}\\3^{\frac{1}{2}}3^{\frac{1}{10}}$

Then, we sum exponents to get the simplest form:

$3^{\frac{1}{2}}3^{\frac{1}{10}}=3^{\frac{1}{2}+\frac{1}{10}} =3^{\frac{10+2}{20}}=3^{\frac{12}{20}}  \\\therefore \sqrt{3\sqrt[5]{3}}=3^{\frac{3}{5} }$

Therefore, the right answer is three to the three fifths power.