Square root?

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

5/(5 sqrt( 5))

Multiply the numerator and denominator by sqrt(5)
5*sqrt(5) / [ 5 *sqrt(5) * sqrt(5)
= 5 * sqrt(5) / 25
= sqrt(5) / 5

The second problem is just double the first one.

Answer 2

you get the answer by multipying the square root of five with both the denominator and the numerator...becuase the the simplest form is when you do not have an radicals (squareroot 5) in the denominator, u have to move them to the numerator...here is how it goes...

(5) / (5) (sq 5)

multiply bottom and top by (sq 5)

(5) (sq 5) / (5) (sq 5) (sq 5)

now sq 5 * sq 5 cancels out and becomes just 5 so you have...

(5) (sq 5) / (5) (5)

this comes down to

(5) (sq 5) / (25)

so simplify to get

(sq 5) / (5)
---------------------------------------
you can do the same thing with (10)/ (5) (sq. 5)

multiply :
(10) (sq 5) / (5) (sq 5) (sq 5)
simplify:
(10) (sq 5) / (5) (5)
simplify:
(10) (sq 5) / (25)
reduce:
(2) (sq 5) / (5)


hope this helps...

Answer 3

#1
since: 5=(squr. root 5)^2
then: 5/(5*(squr. root 5)=(squr. root 5)^2/(5*(squr. root 5))
=(squr. root 5)/5
#2
since 10= 2*5
= 2*(squr. root5)^2
then: 10/5*(squr. root 5)=2(squr. root 5)^2/5(squr. root 5)
=2(squr. root 5)/5

Answer 4

5/5rad5 (cancel the 5's)

1/rad5 (multiply by rad5/rad5)

rad5/5