Question

Divide 36√39 and 9√13

Answer 1

Simplify ^3√54

Answer 2

To divide \( 36\sqrt{39} \) by \( 9\sqrt{13} \), follow these steps:

\[
\frac{36\sqrt{39}}{9\sqrt{13}}
\]

First, divide the coefficients:

\[
\frac{36}{9} = 4
\]

Now, write the expression with the square roots:

\[
4 \cdot \frac{\sqrt{39}}{\sqrt{13}}
\]

Using the property of square roots, we can simplify the fraction:

\[
\frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}}
\]

Now simplify \( \frac{39}{13} \):

\[
\frac{39}{13} = 3
\]

Thus,

\[
\sqrt{\frac{39}{13}} = \sqrt{3}
\]

Now, we can combine our results:

\[
4 \cdot \sqrt{3}
\]

The final result is:

\[
4\sqrt{3}
\]

Answer 3

To simplify \( \sqrt[3]{54} \), we start by factoring 54 into its prime factors:

\[
54 = 2 \times 3^3
\]

Now we can write \( \sqrt[3]{54} \) using these factors:

\[
\sqrt[3]{54} = \sqrt[3]{2 \times 3^3}
\]

We can separate the cube root:

\[
\sqrt[3]{54} = \sqrt[3]{2} \times \sqrt[3]{3^3}
\]

The cube root of \( 3^3 \) is simply 3:

\[
\sqrt[3]{3^3} = 3
\]

Now, we can combine these results:

\[
\sqrt[3]{54} = 3 \times \sqrt[3]{2}
\]

Therefore, the simplified form of \( \sqrt[3]{54} \) is:

\[
3\sqrt[3]{2}
\]