Question

Which number is equivalent to:6√10 * 3√9? (1point)
9√90
9√19
54√10
180√9

Answer 1

To find the equivalent number for \( 6\sqrt{10} \times 3\sqrt{9} \), we can simplify the expression step-by-step.

1. First, multiply the coefficients (the numbers outside the square roots):
\[
6 \times 3 = 18
\]

2. Next, multiply the square roots:
\[
\sqrt{10} \times \sqrt{9} = \sqrt{10 \times 9} = \sqrt{90}
\]

3. Now, combine the results:
\[
18 \sqrt{90}
\]

Next, we can also simplify \(\sqrt{90}\):
\[
\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}
\]

So, substituting back:
\[
18\sqrt{90} = 18 \times 3\sqrt{10} = 54\sqrt{10}
\]

Now we can choose the correct equivalent number from the options given:

- \( 9\sqrt{90} \)
- \( 9\sqrt{19} \)
- \( 54\sqrt{10} \)
- \( 180\sqrt{9} \)

The answer is:
\[
54\sqrt{10}
\]