Question

What is 12−−√
simplified?

Answer 1

What is 54−−√3
simplified?

Answer 2

What is −72−−−−√3
simplified?

Note: You will find the option to add a cubic root symbol in the Algebra (×)
keyboard.

Answer 3

The expression \( \sqrt{12} \) can be simplified by breaking it down into its prime factors.

First, we can express \( 12 \) as \( 4 \times 3 \). Since \( 4 \) is a perfect square, we can simplify as follows:

\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]

So, the simplified form of \( \sqrt{12} \) is \( 2\sqrt{3} \).

Answer 4

To simplify the expression \( \sqrt{54} \), we can start by breaking down \( 54 \) into its prime factors.

We can express \( 54 \) as:

\[
54 = 9 \times 6 = 3^2 \times 6
\]

Now we can find the square root:

\[
\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}
\]

Thus, the simplified form of \( \sqrt{54} \) is \( 3\sqrt{6} \).

Answer 5

To simplify the expression \( \sqrt[3]{-72} \), we start by breaking down \( -72 \) into its prime factors:

\[
-72 = -1 \times 72 = -1 \times 8 \times 9 = -1 \times 2^3 \times 3^2
\]

Next, we apply the properties of cube roots. The cube root of a product is the product of the cube roots, and we can separate out the negative sign:

\[
\sqrt[3]{-72} = \sqrt[3]{-1 \times 2^3 \times 3^2} = \sqrt[3]{-1} \times \sqrt[3]{2^3} \times \sqrt[3]{3^2}
\]

Now, we simplify each part:

1. \( \sqrt[3]{-1} = -1 \)
2. \( \sqrt[3]{2^3} = 2 \)
3. \( \sqrt[3]{3^2} = \sqrt[3]{9} \)

Putting it all together:

\[
\sqrt[3]{-72} = -1 \times 2 \times \sqrt[3]{9} = -2\sqrt[3]{9}
\]

Thus, the simplified form of \( \sqrt[3]{-72} \) is:

\[
\boxed{-2\sqrt[3]{9}}
\]