Can someone show me how to solve this? I'm confused because I don't know how to solve it when there is a square root on the top and bottom

15√6
------
3√5

Question

Can someone  show me how to solve this? I'm confused because I don't know how to solve it when there is a square root on the top and bottom

15√6
------
 3√5

anonymous · Answer

I'm supposed to rationalize and simplify

jhonyy9 · Answer

so try it what you have supposed

jhonyy9 · Answer

courage

anonymous · Answer

I don't know how to rationalize and simplify when there is a square root thing on the top and the bottom @jhonyy9

johnweldon1993 · Answer

Try multiplying both the top and bottom by squareroot5

anonymous · Answer

okay, so I got  15√30                is that right?
                      ------ 
                          8

johnweldon1993 · Answer

Not quite..what happened on the bottom there?

$$3\sqrt{5} \times \sqrt{5} = 3 * 5= 15$$

jhonyy9 · Answer

how you have got this 8 ?

anonymous · Answer

but aren't you supposed to multiply the √5 by the other √5 and the that would be √25 witch would equal 5 and 3+5=8

johnweldon1993 · Answer

All of this is multiplication,where did that + sign come in ?

johnweldon1993 · Answer

$$\large \frac{15\sqrt{6}}{3\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{15\sqrt{6}\sqrt{5}}{3\sqrt{5}\sqrt{5}} = \frac{15 \sqrt{30}}{3 \times 5} = \frac{15\sqrt{30}}{15}$$

Right?

anonymous · Answer

I'm not seeing how 3√5 (√5) is 15....  shouldn't the fives be multiplied together?

3√5(√5) ->  3√25 ->  3√5(5)  -> 3+5=8

johnweldon1993 · Answer

Alright, so from

$$\large 3\sqrt{5}\sqrt{5} = 3\sqrt{5\times 5} = 3\sqrt{25}$$

And yes...the square root of 5 IS 5...but why are you putting a '+' sign? right now it is 3 TIMES the square root of 25...so when that changes to 5 it will be 3 TIMES 5 ...there is no '+' sign added when you simplify a square root

$$\large 3\sqrt{25} = 3 \times 5 = 15$$

anonymous · Answer

ohhhh I see it now! so now that I have   15√30 can I simplify it more?
                                                          -----
                                                             15

johnweldon1993 · Answer

Yes absolutely!

anonymous · Answer

so then I would divide it by 15?

johnweldon1993 · Answer

correct! don't turn it into a decimal though that would be messy..I would just keep it as the radical

anonymous · Answer

okay then, tell me if i'm doing this right...

15√30
-------  =  √30?
    15

johnweldon1993 · Answer

That's perfect!

$$\frac{\cancel{15}\sqrt{30}}{\cancel{15}} = \sqrt{30}$$

anonymous · Answer

Thanks so much for the help!

johnweldon1993 · Answer

No problem!