Question

What is the product of the following expression in simplest radical form?
2√12 x √27 x 2√25

Answer 1

To simplify the expression \( 2\sqrt{12} \times \sqrt{27} \times 2\sqrt{25} \), we will simplify each radical first and then multiply.

Starting with each term:

1. Simplifying \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
Therefore,
\[
2\sqrt{12} = 2 \times 2\sqrt{3} = 4\sqrt{3}
\]

2. Simplifying \( \sqrt{27} \):
\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\]

3. Simplifying \( \sqrt{25} \):
\[
\sqrt{25} = 5
\]
Therefore,
\[
2\sqrt{25} = 2 \times 5 = 10
\]

Now we can substitute back into the original expression:
\[
2\sqrt{12} \times \sqrt{27} \times 2\sqrt{25} = 4\sqrt{3} \times 3\sqrt{3} \times 10
\]

Next, we will multiply these terms:
1. First, multiply the coefficients:
\[
4 \times 3 \times 10 = 120
\]

2. Now multiply the radical parts:
\[
\sqrt{3} \times \sqrt{3} = \sqrt{3^2} = 3
\]

Now combine these results:
\[
120 \times 3 = 360
\]

Thus, the product of the expression in simplest radical form is:
\[
\boxed{360}
\]