How do you simplify sqrt5(3sqrt5-4sqrt3)?

Aug 8, 2018

$15 - 4 \sqrt{15}$

Explanation:

$\text{using the "color(blue)"laws of radicals}$

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

•color(white)(x)sqrtaxxsqrta=(sqrta)^2=a

$\text{distribute the bracket}$

$= 3 {\left(\sqrt{5}\right)}^{2} - 4 \sqrt{5 \times 3}$

$= \left(3 \times 5\right) - 4 \sqrt{15} = 15 - 4 \sqrt{15}$