The ratio x : 64 is equivalent to the ratio 64 : x². What is that value of x?

Set up proportion: Set up the proportion based on the given ratios. The given ratios are x : 64 and 64 : x². Since they are equivalent, we can write the proportion as x/64 = 64/x².Cross-multiply to solve: Cross-multiply to solve for x. Cross-multiplying gives us x * x² = 64 * 64.Simplify the equation: Simplify the equation. Simplifying the left side of the equation by multiplying x by x² gives us x³ = 64 * 64.Calculate value: Calculate the value of 64 * 64. 64 * 64 equals 4096, so the equation now is x³ = 4096.Take cube root: Take the cube root of both sides to solve for x. Taking the cube root of 4096 gives us x = 16, since 16 * 16 * 16 = 4096.

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The ratio $x : 64$ is equivalent to the ratio $64 : x^2$ . What is that value of $x$ ?

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Grade 6

Write an equivalent ratio

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Q. The ratio

x : 64

is equivalent to the ratio

64 : x^2

. What is that value of

x

Set up proportion: Set up the proportion based on the given ratios. $\newline$ The given ratios are $x : 64$ and $64 : x^2$ . Since they are equivalent, we can write the proportion as $\frac{x}{64} = \frac{64}{x^2}$ .
Cross-multiply to solve: Cross-multiply to solve for $x$ . Cross-multiplying gives us $x \times x^2 = 64 \times 64$ .
Simplify the equation: Simplify the equation. $\newline$ Simplifying the left side of the equation by multiplying $x$ by $x^2$ gives us $x^3 = 64 \times 64$ .
Calculate value: Calculate the value of $64 \times 64$ . $\newline$ $64 \times 64$ equals $4096$ , so the equation now is $x^3 = 4096$ .
Take cube root: Take the cube root of both sides to solve for $x$ . $\newline$ Taking the cube root of $4096$ gives us $x = 16$ , since $16 \times 16 \times 16 = 4096$ .