Question

Simplify the radical expression by rationalizing the denominator. Can someone please help me and explain how to do this? I don't understand how to solve the problem.

Answer 1

@campbell_st @aaronq

Answer 2

start my simplifying the radicals...

\[\frac{\sqrt{25}}{\sqrt{50}} = \sqrt{\frac{25}{50}} = \frac{1}{\sqrt{2}}\]

now multiply by 1 written in another form

\[\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\]

just multiply it out for the answer.

Answer 3

@DNTU4GETBOUTME
@Campbell_st has given a quick answer but not covered why - if oyu want - try this to take it in easier steps..

Rationalising the denominator usually means multiply it by itself. BUT you therefore also have to multiply the numerator by th esame thing.

SO you could try this

multiply top and bottom of the original by sqrt (50)

\[9\times \frac{ \sqrt{25} }{ \sqrt{50} }\times \frac{ \sqrt{50} }{ \sqrt{50} }\]

See if you can simplify that a little to start with

Answer 4

@cambell_st First time I got 0.5.... So I did it again and got 5.25. I don't even know how I did that.
I suck at square roots

Answer 5

well you need to leave the answer in radical form

\[\frac{9 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{9 \sqrt{2}}{2}\]

Answer 6

I got this.