Question

What is the difference of 32sqrt(5) - 17sqrt(5') (1 point) Ο 15sqrt(5) Ο 15sqrt(0) Ο 49sqrt(5) The radicals cannot be combined using subtraction

Answer 1

Combine the radicals using addition and subtraction, if possible. 9sqrt(24) - 5sqrt(6) + 3sqrt(54) (1 point) Ο 22sqrt(6) Ο 4sqrt(6) Unlike radicals cannot be combined using addition and subtraction. 42sqrt(2)

Answer 2

To simplify \( 32\sqrt{5} - 17\sqrt{5} \):

1. Since both terms contain \(\sqrt{5}\), you can combine them by subtracting the coefficients.
2. \( 32 - 17 = 15 \).

Therefore,

\[
32\sqrt{5} - 17\sqrt{5} = (32 - 17)\sqrt{5} = 15\sqrt{5}.
\]

So, the correct answer is:

\[
15\sqrt{5}.
\]

Answer 3

To combine the radicals \( 9\sqrt{24} - 5\sqrt{6} + 3\sqrt{54} \), we'll first simplify each radical:

1. **Simplifying \( \sqrt{24} \)**:
\[
\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}
\]
So,
\[
9\sqrt{24} = 9 \cdot 2\sqrt{6} = 18\sqrt{6}.
\]

2. **Simplifying \( \sqrt{54} \)**:
\[
\sqrt{54} = \sqrt{9 \cdot 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6}
\]
So,
\[
3\sqrt{54} = 3 \cdot 3\sqrt{6} = 9\sqrt{6}.
\]

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

\[
9\sqrt{24} - 5\sqrt{6} + 3\sqrt{54} = 18\sqrt{6} - 5\sqrt{6} + 9\sqrt{6}.
\]

Now, combine the terms involving \(\sqrt{6}\):

\[
(18 - 5 + 9)\sqrt{6} = (18 + 9 - 5)\sqrt{6} = 22\sqrt{6}.
\]

So, the final result is:

\[
22\sqrt{6}.
\]

Thus, the correct answer is:

\[
22\sqrt{6}.
\]