## anonymous 4 years ago How do I simplify this expression: √3 / √3 + √2? The answer is 3 - √6... how?

1. anonymous

is sqrt(2) in the denominator?

2. anonymous

no, there's no root 2 in the denominator

3. ash2326

$$\sqrt 3/( \sqrt 3+ \sqrt 2)$$ now multiply numerator and denominator by $$\sqrt 3- \sqrt 2$$ we have $$\sqrt 3/( \sqrt 3 + \sqrt 2) *( \sqrt 3 - \sqrt 2)/( \sqrt 3 - \sqrt 2)$$ we get $(3-2 \sqrt 6)/( 3-2)$ or $3-2\sqrt 6$

4. ash2326

sorry it'd be $3-\sqrt 6$

5. anonymous

why is it 3 - 2√6?

6. ash2326

ignore the 2 int the last two steps

7. ash2326

did you get??

8. anonymous

but why is it 3 - √6? Did you cancel something?

9. ash2326

when we multiplied $$\sqrt 3 -\sqrt 2$$ in the numerator and denominator , denominator became 1 . and numerator became $3-\sqrt 6$

10. anonymous

can you please show me? I'm still confused about what you just said.. so sorry D:

11. ash2326

|dw:1327812623013:dw|

12. anonymous

It's called multiplying by the conjugate to rationalize the denominator

13. anonymous

I have it on my textbook but it's kind of confusing..

14. anonymous

because (a-b)(a+b)=a^2-b^2. Thus you eliminate the square roots from the denominator

15. anonymous

ohh..

16. ash2326

|dw:1327812809044:dw|

17. ash2326

the numerator will become = 3- $$\sqrt 6$$ denominatorw will be = 3-2= 1

18. ash2326

millie did you get ??

19. anonymous

ohhh.. kind of, aww man.

20. anonymous

why did you square it?

21. ash2326

when ever denominator has the form $$\sqrt a\pm \sqrt b$$ multiply numerator and denominator by $$\sqrt a\mp \sqrt b$$

22. anonymous

ohh, so the opposite.. and then?

23. ash2326

we'd in the denominator $(\sqrt 3 + \sqrt 2)*( \sqrt 3 - \sqrt 2)$ so this is in the form of (a+b)*(a-b)= a^2-b^2 so it'll become $({\sqrt 3}^2 - {\sqrt 2}^2)$ which is 3-2= 1

24. anonymous

ohhh.. it's 3-2= 1? Not 3^2 - 2^2..?

25. ash2326

yeah , square of $$\sqrt a$$ = a

26. anonymous

square root of a number squared is the number itself

27. ash2326

milie you got it??

28. anonymous

yes I did! thank you!

29. ash2326

good :)