Question

Rationalize the denominator and simplify.

a) 5/4- √3
b) 12/√7 + 2
c) 6/√2 - √3
d) 15√6/3√5

Answer 1

a) \[\huge \frac{5}{4-\sqrt3}=\frac{5}{4-\sqrt3} \times \frac{4+\sqrt3}{4+\sqrt3}\]
\[=\frac{5(4+\sqrt3)}{(4-\sqrt3)(4+\sqrt3)}=\frac{20+5 \sqrt3}{16-3}=\frac{20+5 \sqrt3}{13}\]

@JessicaChen

Answer 2

@dpasingh can you help with the other ones?

Answer 3

Well, they are all essentially solved by the same process. Note that all she is doing is getting rid of the square roots in the denominator. To do that she is simply multiplying the bottom and top by the denominator, what that does is create as you can see in the second line on the denominator is \[(4-\sqrt{3})(4+\sqrt{3})\] that makes is so that you get \[(\sqrt{3})^{2}\], and what happens when you have the square root of something to the second power? well they cancel each other leaving you with just "3", after she multiplies everything else she just solves normally. So for the rest all you reall have to do is multiply the denominator by both sides to make the square root number into a squareroot to the second power, then they cancel out and leave you with the plain number so you can solve the rest with no worries.

Answer 4

well actually you get 16-\[(\sqrt{3})^{2}\], but when you cancel out the square root and the square part, you get plain "3"