Question

Simplifying radicals! Please help me & Show WORK

Answer 1

Answer:

Solving the radical $4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})$ we get $\mathbf{-16\sqrt{30}+72}$

Step-by-step explanation:

We need to simplify the radical: $4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})$

Prime factors of 18 are: 2x3x3

Replacing $\sqrt{18}$ with its factors

$4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3\times3})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3^2})$

We know that $\sqrt{3^2}=3$

$=4\sqrt{2}(-4\sqrt{15}+3\times3\sqrt{2})\\=4\sqrt{2}(-4\sqrt{15}+9\sqrt{2})$

Multiplying $4\sqrt{2}$ with terms inside the bracket

$=4\sqrt{2}(-4\sqrt{15})+4\sqrt{2}( 9\sqrt{2}))\\=-16\sqrt{2}\sqrt{15}+36\sqrt{2} \sqrt{2}$

We know that $\sqrt{2} \sqrt{2}=2$

$=-16\sqrt{2*15}+36(2)\\=-16\sqrt{30}+72$

So, solving the radical $4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})$ we get $\mathbf{-16\sqrt{30}+72}$