What is the difference of 8√125−7√80 ?(1 point)

Question

Responses

35–√
3 square root of 5

2110−−−√
2 square root of 110

125–√
12 square root of 5

885–√

Answer 1

To simplify the expression \( 8\sqrt{125} - 7\sqrt{80} \), we start by simplifying each square root.

1. Simplifying \( \sqrt{125} \): \[ \sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5} \] So, \( 8\sqrt{125} = 8 \cdot 5\sqrt{5} = 40\sqrt{5} \).

2. Simplifying \( \sqrt{80} \): \[ \sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \] So, \( 7\sqrt{80} = 7 \cdot 4\sqrt{5} = 28\sqrt{5} \).

Now, we can substitute these simplified forms back into the expression:

\[ 8\sqrt{125} - 7\sqrt{80} = 40\sqrt{5} - 28\sqrt{5} \]

Since both terms share the same radical \( \sqrt{5} \), we can combine them:

\[ 40\sqrt{5} - 28\sqrt{5} = (40 - 28)\sqrt{5} = 12\sqrt{5} \]

Thus, the final result is:

\[ \boxed{12\sqrt{5}} \]