Question

7 squareroot 72 - 5 squareroot 2

Answer 1

To simplify the expression \( 7\sqrt{72} - 5\sqrt{2} \), we start by simplifying \(\sqrt{72}\).

\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}
\]

Now, we substitute this back into the expression:

\[
7\sqrt{72} = 7 \times 6\sqrt{2} = 42\sqrt{2}
\]

Now, we rewrite the original expression:

\[
42\sqrt{2} - 5\sqrt{2}
\]

Next, we can combine the like terms:

\[
(42 - 5)\sqrt{2} = 37\sqrt{2}
\]

Thus, the simplified expression is:

\[
\boxed{37\sqrt{2}}
\]