aubreyrve one year ago MEDALS FOR BEST RESPONSE!!!!! can someone simplify this step by step because I don't understand it 4sqrt(6) over sqrt(30)

1. YanaSidlinskiy

@johnweldon1993 ? This guy is smart!!!:)

2. johnweldon1993

Lol well thank you @YanaSidlinskiy :) $\large \frac{4\sqrt{6}}{\sqrt{30}}$ Can be seen as $\large 4 \times \sqrt{\frac{6}{30}}$ Does that help at all?

3. johnweldon1993

Because remember $\large \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$

4. aubreyrve

No, I still don't understand that sorry can you brake it down or something? @johnweldon1993

5. YanaSidlinskiy

6. johnweldon1993

Yeah sure... $\large \frac{4\sqrt{6}}{\sqrt{30}}$ Alright....we can just ignore that 4 for now...why? because it is just multiplying whatever we get as a result... so we can do that later :) So all we have is $\large 4 \times \frac{\sqrt{6}}{\sqrt{30}}$ It IS important to remember rules such as $\large \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ so that means we can turn $\large \frac{\sqrt{6}}{\sqrt{30}} \large {\rightarrow} \sqrt{\frac{6}{30}}$ alright?

7. johnweldon1993

The next step would be...simplify what is inside the radical... *hint...looks like each number is divisible by 6*

8. johnweldon1993

Alright well since I see you have left..I'll just keep going here to help out anyone who might need it... so we now have $\large 4 \times \sqrt{\frac{6}{30}}$ Lets simplify that radical....both numbers are divisible by 6.... What is 6 divided by 6? 1 what is 30 divided by 6? 5 So now we have $\large 4 \times \sqrt{\frac{1}{5}}$ Remember that little rule we wrote above? $\large \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ This means we can work backwards this time...and write $\large \sqrt{\frac{1}{5}} \rightarrow \frac{\sqrt{1}}{\sqrt{5}}$ So NOW we have $\large 4 \times \frac{\sqrt{1}}{\sqrt{5}}$ Just 1 little simplification here...what is the square root of 1? Just 1 ...so we have $\large 4 \times \frac{1}{\sqrt{5}}$ And finally we multiply that by 4...to get $\large \frac{4}{\sqrt{5}}$

9. YanaSidlinskiy

Told you!!! He's smart!!

10. aubreyrve

ok, thank you I understand @johnweldon1993