Question

Which is equivalent to √60n^11/256n^4 after it has been simplified completely? Assume n =0

Answer 1

the second option

Explanation:

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Answer 2

`\large\boxed{(n^3)/(8)√(15n)}`

Explanation:

`\sqrt{(60n^(11))/(256n^4)}\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\ \text{and}\ \sqrt{(a)/(b)}=(√(a))/(√(b))\\\\=\sqrt{(60)/(256)n^(11-4)}=(√(60n^7))/(√(256))=\frac{\sqrt{4n^(6+1)\cdot15}}{16}\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=(√(4n^6\cdot15n))/(16)\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=\frac{\sqrt{4n^(3\cdot2)}\cdot√(15n)}{16}\qquad\text{use}\ (a^n)^m=a^(nm)`

`=(√(4(n^3)^2)\cdot√(15n))/(16)=(√(4)\cdot√((n^3)^2)\cdot√(15n))/(16)=(2\!\!\!\!\diagup^1√(15n))/(16\!\!\!\!\!\diagup_8)=(n^3√(15n))/(8)`