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}}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B36%20a%5E%7B8%7D%7D%7B225%20a%5E%7B2%7D%7D%7D)
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}}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B2%282%29%282%29%283%29%283%29%5Cleft%28a%5E%7B8%7D%5Cright%29%7D%7B3%283%29%285%29%285%29%5Cleft%28a%5E%7B2%7D%5Cright%29%7D%7D%3D%5Csqrt%7B%5Cfrac%7B36%20a%5E%7B8%7D%7D%7B225%20a%5E%7B2%7D%7D%7D)
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
which is not equivalent to ![\sqrt{\frac{36 a^{8}}{225 a^{2}}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B36%20a%5E%7B8%7D%7D%7B225%20a%5E%7B2%7D%7D%7D)
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
which is not equivalent to ![\sqrt{\frac{36 a^{8}}{225 a^{2}}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B36%20a%5E%7B8%7D%7D%7B225%20a%5E%7B2%7D%7D%7D)
Hence, Option C is not the correct answer.
Option D: "StartFraction 6 Over 15 EndFraction a Superscript 4" which can be written as
which is not equivalent to ![\sqrt{\frac{36 a^{8}}{225 a^{2}}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B36%20a%5E%7B8%7D%7D%7B225%20a%5E%7B2%7D%7D%7D)
Hence, Option D is not the correct answer.
Option E: "Two-fifths a cubed" which can be written as
which is not equivalent to ![\sqrt{\frac{36 a^{8}}{225 a^{2}}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B36%20a%5E%7B8%7D%7D%7B225%20a%5E%7B2%7D%7D%7D)
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.