Respuesta :

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

[tex]\frac{60n^{11} }{256n^{4} }[/tex]

Simplify constant terms and n terms separately to get

=[tex]\frac{15n^7}{64} \\=\frac{n^3}{8} \sqrt{15n}[/tex]

Out of the four options option 2 matches with this.

Hence correct answer is option B.

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

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

[tex]\sqrt{\frac{15n^{11}}{64n^4}}[/tex]

Using exponent property [tex]\frac{a^b}{a^c}=a^{b-c}[/tex], we will get:  

[tex]\sqrt{\frac{15n^{(11-4)}}{64}[/tex]          

[tex]\sqrt{\frac{15n^{7}}{64}[/tex]

Now we will use exponent property [tex]\sqrt{\frac{a^b}{a^c}}=\frac{\sqrt{a^b}}{\sqrt{a^c}}[/tex].

[tex]\frac{\sqrt{15n^7}}{\sqrt{64}}[/tex]

[tex]\frac{\sqrt{15n\cdot n^6}}{\sqrt{8^2}}[/tex]

[tex]\frac{\sqrt{15n\cdot (n^3)^2}}{\sqrt{8^2}}[/tex]

Now we will bring out perfect squares from radical as:

[tex]\frac{n^3\sqrt{15n}}{8}[/tex]

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