Divide 36√39 and 9√13

Answer 1

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 2

Simplify ^3√54

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:

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