How do you rationalize the denominator and simplify (4sqrt5)/(3sqrt5+2sqrt2)?

May 2, 2017

$\frac{1}{37} \left(60 - 8 \sqrt{10}\right)$

Explanation:

To rationalize the denominator multiply by $\left(3 \sqrt{5} - 2 \sqrt{2}\right)$ in both numerator and denominator. we get ,

((4sqrt5)* (3sqrt5-2sqrt2))/((3sqrt5+2sqrt2)*(3sqrt5-2sqrt2)

$= \frac{12 \cdot 5 - 8 \cdot \sqrt{10}}{{\left(3 \sqrt{5}\right)}^{2} - {\left(2 \sqrt{2}\right)}^{2}} = \frac{60 - 8 \sqrt{10}}{45 - 8}$

$= \frac{60 - 8 \sqrt{10}}{37} = \frac{1}{37} \left(60 - 8 \sqrt{10}\right)$ [Ans]

May 2, 2017

we can multiply the fraction by 1 to rationalise the denominator

Explanation:

$\frac{4 \sqrt{5}}{3 \sqrt{5} + 2 \sqrt{2}}$$\times \frac{3 \sqrt{5} - 2 \sqrt{2}}{3 \sqrt{5} - 2 \sqrt{2}}$

This gives $\frac{60 - 8 \sqrt{10}}{45 - 8}$

i think the remaining workings should be quite easy to complete