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If x=8sqrt(3) and 3x=sqrt(3y), what is t...

If `x=8sqrt(3) and 3x=sqrt(3y)`, what is the value of y?

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Difficult: Medium
Category: Passport to Advanced Math/ Exponents
Strategic Advice: You can "separate" radical expressions as long as the only operations involved are multiplication and division. For example, `sqrt(3y)=sqrt(3)sqrt(y)` because y is being multiplied by 3.
Getting to the Answer: First, substitute `8sqrt(3)` for x into the equation and simplify. Next, write`sqrt(3y)` as `sqrt(3)sqrt(y)` so you can divide both sides by `sqrt(3)`. Finally, square both sides to eliminate the radical:
`3x=sqrt(3y)`
`3(8sqrt(3))=sqrt(3y)`
`24sqrt(3)=sqrt(3)sqrt(y)`
`24=sqrt(y)`
`y=24^(2)`
Squaring 24, the final answer is 576.
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