Square roots?

Question

Hi,
I'm doing evaluating trigonometric functions and the answer can not be left as a decimal so,
if I get an answer like
5/(5 squareroot of 5) how is it in the simplest form?
the book says:

(squr. root of 5) / 5

How did they get that?

The same thing with 10 / (5 sqr. root 5)
to which the answer is said to be (2 sqr. root 5) / 5

How did they get the #1 and #2 que.

A big thank you!

Answer 1

You want to get the sqrt out of the denominator.
You do this by multiplying the entire fraction by 1, where 1 = sqrt5/sqrt5.
So, for numerator: you get 5 *sqrt5
denominator: 5*sqrt5*sqrt5
= 5*5 = 25
Now, simplify the entire fraction: 5*sqrt5/25
= sqrt5/5

Do a similar process for the second one:
numerator: 10*sqrt5
denom: 5*sqrt5*sqrt5
= 5*5 = 25
Simplify: 10sqrt5/25
= 2sqrt5/5

Answer 2

They do this by a process called rationalizing the denominator. By multiplying the numerator and denominator by the denominator, the radical number is eliminated in the denominator. Here's an example:

1/√x = ?

Multiply both numerator and denominator by the denominator:

1/√x = (1/√x)(√x/√x) = √x / (√x /√x) = √x / (√x)² = √x / x.

Answer 3

5/√5

Multiply both numerator and denominator by √5

(5(√5))/((√5)(√5))

and you have √5/5

Generally you should always clear the denominator of an answer of any radicals.
.