Question

What is −72−−−−√3 simplified? Note: You will find the option to add a cubic root symbol in the Algebra (×) keyboard.

Answer 1

To simplify the expression \(-72\sqrt{3}\), we first express \( -72 \) as \( -1 \times 72 \).

Next, we notice that \( 72 \) can be factored into \( 36 \times 2 \), where \( 36 \) is a perfect square.

So we have:

\[
-72\sqrt{3} = -1 \times 72\sqrt{3} = -1 \times (36 \times 2)\sqrt{3}
\]

Now let's simplify it:

\[
-1 \times (36\sqrt{3} \times 2) = -2 \times 36\sqrt{3} = -2 \times 6\sqrt{12} = -12\sqrt{12}
\]

We can also simplify \(\sqrt{12}\):

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

So,

\[
-12\sqrt{12} = -12 \times 2\sqrt{3} = -24\sqrt{3}
\]

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

\[
-24\sqrt{3}
\]

The expression after full simplification remains as:

\[
-24\sqrt{3}
\]

So the answer you are looking for is \( -24\sqrt{3} \).