Question

-7 squareroot 33 + 10 squareroot 132

Answer 1

To simplify the expression \(-7 \sqrt{33} + 10 \sqrt{132}\), we first simplify \(\sqrt{132}\).

We can factor \(132\) as follows:
\[
132 = 4 \times 33
\]
Taking the square root of \(132\), we have:
\[
\sqrt{132} = \sqrt{4 \times 33} = \sqrt{4} \times \sqrt{33} = 2 \sqrt{33}
\]

Now we substitute \(\sqrt{132}\) back into the expression:
\[
-7 \sqrt{33} + 10 \sqrt{132} = -7 \sqrt{33} + 10(2 \sqrt{33})
\]
This simplifies to:
\[
-7 \sqrt{33} + 20 \sqrt{33}
\]

Now, we combine the like terms:
\[
(-7 + 20) \sqrt{33} = 13 \sqrt{33}
\]

Thus, the simplified expression is:
\[
\boxed{13 \sqrt{33}}
\]