Question

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

Answer 1

C)
`6√(5)`

Arithmetic without explanation:

`2√(3)* √(15)\\ = 2√(3)* √(3*5) \\ = 2√(3^2) *√(5) \\ = 2 * 3√(5) \\= 6√(5)`

Example of radical multiplication:

Take
`y√(x) * a√(b)` as an example:

1. Multiple the numbers inside the roots

`√(x) * √(b) = √(x*b) = √(xb)`

2. Multiple the numbers outside the roots

`y*a = ya`

3. Combine them and simplify

`ya√(xb)`

Explanation:

We are given the expression
`2√(3)*√(15)`

1. Identify the roots and multiply them

The roots are
`√(3)` and
`√(15)`

`√(3) *√(15) \\= √(45)`

2. Multiply the numbers outside the root

For
`2√(3)` it is
`2` and for
`√(15)` it is
`1`

`2*1 = 2`

3. Combine and simplify

Combine:

`2* √(45)\\= 2√(45)`

Simplify:

*Note:
`√(n^2) = n`

1. Find the Prime factorization of 45

`45 = 3^2 * 5`

2. Simplify the Root

`2√(45) \\ = 2√(3^2 * 5) \\= 2√(3^2) * √(5) \\= 2 * 3√(5)\\ =6√(5)`

We end up with
`6√(5)`

Answer 2

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.