Question

Can I get some help, please?

Answer 1

Let's keep in mind that 

$\bf \sqrt{\cfrac{36a^8}{225a^2}}\implies \sqrt{\cfrac{6^2a^{4\cdot 2}}{15^2a^2}}\implies \sqrt{\cfrac{6^2(a^4)^2}{15^2a^2}}\implies \cfrac{6a^4}{15a}\implies \cfrac{2a^3}{5}$

A)

$\bf \sqrt{\cfrac{2(2)(3)(3)aaaaaaaa}{3(3)(5)(5)aa}}\implies \sqrt{\cfrac{36a^{1+1+1+1+1+1+1+1}}{225a^{1+1}}}\implies \sqrt{\cfrac{36a^8}{225a^2}}$

B)

$\bf \sqrt{\cfrac{4a^6}{25}} \implies \sqrt{\cfrac{2^2a^{3\cdot 2}}{5^2}}\implies \sqrt{\cfrac{2^2(a^3)^2}{5^2}}\implies \cfrac{2a^3}{5}$

C)

$\bf \cfrac{6}{25}\sqrt{\cfrac{a^8}{a^2}}\implies \cfrac{6}{25}\sqrt{a^8\cdot a^{-2}}\implies \cfrac{2}{5}\sqrt{a^{8-2}}\implies \cfrac{2}{5}\sqrt{a^6} \\\\\\ \cfrac{2}{5}\sqrt{a^{3\cdot 2}}\implies \cfrac{2}{5}\sqrt{(a^3)^2}\implies \cfrac{2}{5}a^3\implies \cfrac{2a^3}{5}$

D)

$\bf \cfrac{6}{15}a^4\implies \cfrac{2}{5}a^4\implies \cfrac{2a^4}{5}~~\ne ~~\cfrac{2a^3}{5}$

E)

well, by now, just check above, you'd know.