Question

A. StartRoot StartFraction 2 (2) (3) (3) (a) (a) (a) (a) (a) (a) (a) (a) Over 3 (3) (5) (5) (a) (a) EndFraction EndRoot

Answer 1

Option A. StartRoot StartFraction 2 (2) (3) (3) (a) (a) (a) (a) (a) (a) (a) (a) Over 3 (3) (5) (5) (a) (a) EndFraction EndRoot

Step-by-step explanation:

From all the five options, we need to find the expression which is equivalent to $\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Option A: "StartRoot StartFraction 2 (2) (3) (3) (a) (a) (a) (a) (a) (a) (a) (a) Over 3 (3) (5) (5) (a) (a) EndFraction EndRoot" which can be written as

$\sqrt{\frac{2(2)(2)(3)(3)\left(a^{8}\right)}{3(3)(5)(5)\left(a^{2}\right)}}=\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Hence, Option A is the correct answer.

Option B: "StartRoot StartFraction 4 a Superscript 6 Baseline Over 25 EndFraction EndRoot" which can be written as

$\sqrt{\frac{4a^{6} }{25} }$ which is not equivalent to $\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Hence, Option B is not the correct answer.

Option C: "StartFraction 5 Over 25 EndFraction StartRoot StartFraction a Superscript 8 Over a squared EndFraction EndRoot" which can be written as

$\frac{5}{25} \sqrt \frac{a^{8} }{a^{2} }$ which is not equivalent to $\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Hence, Option C is not the correct answer.

Option D: "StartFraction 6 Over 15 EndFraction a Superscript 4" which can be written as

$\frac{6}{15} a^{4}$ which is not equivalent to $\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Hence, Option D is not the correct answer.

Option E: "Two-fifths a cubed" which can be written as

$\frac{2}{5} a^{3}$ which is not equivalent to $\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Hence, Option E is not the correct answer.

Hence, the correct option is A.

Thus, the expression is equivalent to StartRoot StartFraction 2 (2) (3) (3) (a) (a) (a) (a) (a) (a) (a) (a) Over 3 (3) (5) (5) (a) (a) EndFraction EndRoot.