Question

Calculate 3√2 × 2√8 × √3 × √6.

A) 24√6
B) 24
C) 72√6
D) 18√6

Answer 1

To calculate the expression involving multiple square roots, you can simplify each radical and then multiply the simplified radicals together. The final answer is 72.

Step-by-step explanation:

To solve this expression, we can simplify each radical first:

√2 = √(2∙1) = √2 = √2

√8 = √(4∙2) = √4√2 = 2√2

√3 x √6 = √(3∙6) = √18

Now we can multiply the simplified radicals:

3√2 x 2√8 x √3 x √6 = 3(√2) x 2(2√2) x √18 = 6√2√2 x √18 = 6(2) x √2 x √18 = 12 x √36 = 12 x 6 = 72

The final answer is 72, so the correct option is B.