Question

NEED HELP ANSWERING THIS QUESTION

Answer 1

`\large\boxed{B.\ (x\sqrt2)/(2y)}`

Explanation:

`√(9x^2):√(18y^2)=(√(9x^2))/(√(18y^2))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=(\sqrt9\cdot√(x^2))/(√(18)\cdot√(y^2))\qquad\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=(3\cdot x)/(√(9\cdot2)\cdot y)=(3x)/(\sqrt9\cdot\sqrt2\cdot y)=(3x)/(3y\sqrt2)\qquad\text{cancel 3}\\\\=(x)/(y\sqrt2)\cdot(\sqrt2)/(\sqrt2)\qquad\text{use}\ √(a)\cdot√(a)=a\\\\=(x\sqrt2)/(2y)`

Answer 2

B.
`(x√(2))/(2y)`

Explanation:

We want to divide
`√(9x^2)` by
`√(18y^2)`.

This becomes:

`(√(9x^2))/(√(18y^2))`

`(√((3x)^2))/(√(2(3y)^2))`

We remove the perfect squares to obtain

`(3x)/(3y√(2))`

Cancel out the common factors to get;

`(x)/(y√(2))`

Rationalize the denominator to get:

`(x)/(y√(2))* (√(2))/(√(2))`

`(x√(2))/(2y)`

The correct answer is B