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love history [14]
3 years ago
6

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

Mathematics
2 answers:
Tema [17]3 years ago
4 0

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).

bogdanovich [222]3 years ago
3 0

Answer:

<h2><em>Three to the three fifths power.</em></h2>

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 <em>three to the three fifths power.</em>

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