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The ratio x:8 is equivalent to the ratio 27:x^2. What is the value of x?

The ratio x:8 is equivalent to the ratio 27:x^2. What is the value of x?-example-1

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We are given that the following ratios are equivalent:


\begin{gathered} x\colon8 \\ 27\colon x^2 \end{gathered}

This means that the following relationship holds:


(x)/(8)=(27)/(x^2)

Now, to solve for "x" we can cross multiply the equation:


x* x^2=27*8

Solving the operations:


x^3=216

Now we take the cubic root to both sides:


x=\sqrt[3]{216}

Solving the operation:


x=6

Therefore, the value of "x" is 6.

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