Subtract √75−√45.(1 point) The difference is .

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 days ago

To subtract \( \sqrt{75} - \sqrt{45} \), we can simplify each square root first.

1. Simplify \( \sqrt{75} \):
\[
\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
\]

2. Simplify \( \sqrt{45} \):
\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
\]

Now we can rewrite the original expression:
\[
\sqrt{75} - \sqrt{45} = 5\sqrt{3} - 3\sqrt{5}
\]

Since \( 5\sqrt{3} \) and \( 3\sqrt{5} \) are not like terms, we cannot simplify it further.

Thus, the difference is:
\[
\boxed{5\sqrt{3} - 3\sqrt{5}}
\]