Question

Simplify.

√ 28⋅√ 27⋅√ 5

A.) 6√ 15

B.) 7√ 15

C.) 7√ 105

D.) 6√ 105

Answer 1

√28 × √27 × √5 =
√28×27×5=
√3780=
√6^2 × √105=
6√105

The asnwer is D

Answer 2

D)
`6√(105)`

Explanation:

The square root is a function that is distributed for the product and the division.

For example :

`(√(3)).(√(6))=√((3).(6))=√(18)`

First we need to factorize the numbers in the square roots ⇒

`28=(2^(2)).(7)`

`27=3^(3)`

`5=5`

Now we replace this in the expression :

`\sqrt{(2^(2)).(7)}\sqrt{3^(3)}√(5)`

Then we distribute the square root (remember that
`3^(3)=(3^(2)).(3)`

⇒

`\sqrt{(2^(2)).(7)}\sqrt{(3^(2)).(3)}√(5)=\sqrt{2^(2)}√(7)\sqrt{3^(2)}√(3)√(5)`

This expression is equivalent to

`(2).(√(7)).(3)(√(3)).(√(5))=(6).√(7)√(3)√(5)=(6).√((7).(3).(5))=6√(105)`

Notice that in the last step we did the inverse operation.

The answer is D)
`6√(105)`