Question

how do you solve this 3+4sqrt15(4+3sqrt15)<-----multiply by conjugate
4-3sqrt15(4+3sqrt15) i know that you foil it ,but im not doing something right

Answer 1

Is that supposed to be \[\frac{(3+4\sqrt{15})(4+3\sqrt{15})}{(4-3\sqrt{15})(4+3\sqrt{15})}\]?

Answer 2

correct not sure how u got it to look like that but yes can u work it out step by step guess im a lil rusty on foil method

Answer 3

I'll multiply something similar:
\[(1+2\sqrt{3})(2+\sqrt{3}) = 1(2+\sqrt{3})+2\sqrt{3}(2+\sqrt{3})\]\[\qquad = 1*2 + 1*\sqrt{3} + 2\sqrt{3}*2 + 2\sqrt{3}*\sqrt{3}\]\[\qquad=2+\sqrt{3}+4\sqrt{3}+2*3\]\[\qquad=8+5\sqrt{3}\]

Answer 4

I dislike FOIL because it doesn't work for anything but binomials. I use the distributive property instead.

Answer 5

The blue Equation button at the bottom left will allow you to typeset your math expressions once you figure it out.

Answer 6

thanks its sucks being a visual learner

Answer 7

The denominator is easier when you are multiplying by the conjugate as you are here: it's just the first thing squared plus the second thing squared:

\[(a+b)(a-b) = a(a-b)+b(a-b) = a*a -a*b + b*a -b*b = a^2 - b^2\]

So for yours:
\[(4-3\sqrt{15})(4+3\sqrt{15}) = 4^2-(3\sqrt{15})^2 \]\[\qquad= 4*4 - 3*3*\sqrt{15}*\sqrt{15} = 16-9*15 = 16-135\]\[\qquad = -119\]
With a little practice, you could just write \(16-9*15 =-119\)