Question

Need help with algebra 2b question! see attachment.

Answer 1

\(\color{black}{\displaystyle \frac{\sqrt{3x^{12}y^{10}} }{\sqrt{5x^6y^3}} }\)

Answer 2

This could be broken down into product inside the root, and then into the product of roots.

Answer 3

\(\color{black}{\displaystyle \frac{\sqrt{3\times x^{6+6} \times y^{5+5}} }{\sqrt{5\times x^{3+3}\times y^{2+1}}} }\)

\(\color{black}{\displaystyle \frac{\sqrt{3\times x^{6}x^6 \times y^5y^5} }{\sqrt{5\times x^{3}x^3\times y^{2}y^1}} }\)

\(\color{black}{\displaystyle \frac{\sqrt{3}\times \sqrt{x^{6}x^6} \times \sqrt{y^5y^5} }{\sqrt{5}\times \sqrt{x^{3}x^3}\times \sqrt{y^{2}y^1}} }\)

\(\color{black}{\displaystyle \frac{\sqrt{3}\times \sqrt{(x^{6})^2} \times \sqrt{(y^5)^2} }{\sqrt{5}\times \sqrt{(x^{3})^2}\times \sqrt{y^{2}}\times \sqrt{y^1}} }\)

Answer 4

you factored is right?

Answer 5

(they are assuming that x and y are positive, so you won't need absolute value)

Answer 6

I am basically using the fact that
\(\color{black}{\displaystyle \sqrt{a\times b}=\sqrt{a}\times \sqrt{b} }\)

and the rule that:
\(\color{black}{\displaystyle z^{m+n}=z^m\times z^n }\)

Answer 7

so it is \[x^3y^3\sqrt{15y} / \sqrt{5x^6y^3}\]

Answer 8

@SolomonZelman