Question

Find the product. 2√3•√15 A)5√5 B)√45 C)6√5 D)18√5

Answer 1

First multiply the numbers inside the radicals together.

So √3 · √15 is √45.

So we have 2√45.

Note that the 2 can't be multiplied by anything since

√15 has nothing outside of the radical.

So we have 2√45.

Now, break down your square root.

√45 breaks down as 9 · 5 and 9 breaks down as 3 · 3.

Since we have a pair of 3's, a 3 comes outside of the radical

multiplying by the 2 that was previously outside to get 6.

The 5 doesn't pair up so it stays inside.

So our final answer is 6√5.

Answer 2

Answer:

C) $6\sqrt{5}$

Arithmetic without explanation:

$2\sqrt{3}* \sqrt{15}\\ = 2\sqrt{3}* \sqrt{3*5} \\ = 2\sqrt{3^2} *\sqrt{5} \\ = 2 * 3\sqrt{5} \\= 6\sqrt{5}$

Example of radical multiplication:

Take $y\sqrt{x} * a\sqrt{b}$  as an example:

1. Multiple the numbers inside the roots

      $\sqrt{x} * \sqrt{b} = \sqrt{x*b} = \sqrt{xb}$  

2. Multiple the numbers outside the roots

       $y*a = ya$

3. Combine them and simplify

      $ya\sqrt{xb}$

Step-by-step explanation:

We are given the expression $2\sqrt{3}*\sqrt{15}$

 1. Identify the roots and multiply them

         The roots are $\sqrt{3}$  and $\sqrt{15}$

           $\sqrt{3} *\sqrt{15} \\= \sqrt{45}$

  2. Multiply the numbers outside the root

         For $2\sqrt{3}$ it is $2$ and for $\sqrt{15}$ it is $1$

          $2*1 = 2$

  3. Combine and simplify

    Combine:

              $2* \sqrt{45}\\= 2\sqrt{45}$

   Simplify:

           *Note: $\sqrt{n^2} = n$

        1. Find the Prime factorization of 45

                   $45 = 3^2 * 5$

        2. Simplify the Root

                  $2\sqrt{45} \\ = 2\sqrt{3^2 * 5} \\= 2\sqrt{3^2} * \sqrt{5} \\= 2 * 3\sqrt{5}\\ =6\sqrt{5}$

We end up with $6\sqrt{5}$