Find the product of √6*√12. Should I just multiply them both to get √72, or factor each of them, need explanation

Question

Find the product of √6*√12

Answer 1

Step 1: Multiply √6 and √12. To multiply radicals, we multiply what is inside of the radical together so it will give us √72.

Step 2: Simplify by prime factorization.

The prime factorization of √72 is √2*2*2*3*3.

We take out the number that appears twice because we are taking the square root.

2*3√2

6√2

Answer 2

Yes, you can write √6 * √12 as √72

The general rule is √a * √b = √(a*b), or

"The product of square roots is the square root of the product".

You can also write this rule in exponent form, as:

a^1/2 * b^1/2 = (a*b)^1/2,

or, more generally, as

aⁿ * bⁿ = (a*b)ⁿ

and then do the prime factorization to turn √72 into √36 * √2, or 6 * √2

Answer 3

Another way:

Factor √12 to get √6 * √2

Now you have √6 * √6 * √2 = 6√2