Question

Which is equivalent to after it has been simplified completely? Assume n ≠ 0. PICTURE BELOW

Answer 1

Answer:

Option B

Step-by-step explanation:

Given is a term under square root sign.

Inside square root is given a rational function in n as

$\frac{60n^{11} }{256n^{4} }$

Simplify constant terms and n terms separately to get

=$\frac{15n^7}{64} \\=\frac{n^3}{8} \sqrt{15n}$

Out of the four options option 2 matches with this.

Hence correct answer is option B.

Answer 2

We have been given an expression $\sqrt{\frac{60n^{11}}{256n^4}}$. We are asked to simplify our given expression.  

First of all, we will simplify the expression inside radical as:

$\sqrt{\frac{15n^{11}}{64n^4}}$

Using exponent property $\frac{a^b}{a^c}=a^{b-c}$, we will get:  

$\sqrt{\frac{15n^{(11-4)}}{64}$          

$\sqrt{\frac{15n^{7}}{64}$

Now we will use exponent property $\sqrt{\frac{a^b}{a^c}}=\frac{\sqrt{a^b}}{\sqrt{a^c}}$.

$\frac{\sqrt{15n^7}}{\sqrt{64}}$

$\frac{\sqrt{15n\cdot n^6}}{\sqrt{8^2}}$

$\frac{\sqrt{15n\cdot (n^3)^2}}{\sqrt{8^2}}$

Now we will bring out perfect squares from radical as:

$\frac{n^3\sqrt{15n}}{8}$

Therefore, simplified form of our given expression would be $\frac{n^3\sqrt{15n}}{8}$ and option B is the correct choice.