Multiply / Divide Radical Expressions.

Question

What is the product of √6 and 9√12 in simplest radical form?

Answer 1

To find the product of √6 and 9√12, we multiply the coefficients and then multiply the radicands:

√6 * 9√12
= 9 * √6 * √12

Since √6 * √12 is equal to the square root of the product of the radicands, we have:

= 9 * √(6 * 12)
= 9 * √72

To simplify √72, we look for perfect square factors. The largest perfect square that divides 72 is 36, which is a factor of 72. Therefore:

√72 = √(36 * 2) = √36 * √2 = 6√2

Substituting this back into the expression, we get:

9 * 6√2 = 54√2

Therefore, the product of √6 and 9√12 in simplest radical form is 54√2.