Question

which equation has a solution that is greater than 6?
$x^3 = 216$
$x^2 = 40$
$x^2 = 12$
$x^3 = 100$

Explanation:

Step1: Solve \(x^3 = 216\)

Take cube root: \(x=\sqrt[3]{216}=6\)

Step2: Solve \(x^2 = 40\)

Take square root: \(x=\sqrt{40}\approx6.32\) (positive root)

Step3: Solve \(x^2 = 12\)

Take square root: \(x=\sqrt{12}\approx3.46\) (positive root)

Step4: Solve \(x^3 = 100\)

Take cube root: \(x=\sqrt[3]{100}\approx4.64\)

Step5: Compare solutions to 6

• \(x = 6\) (not >6)
• \(x\approx6.32\) (>6)
• \(x\approx3.46\) (not >6)
• \(x\approx4.64\) (not >6)

Answer:

The equation \(x^2 = 40\) has a solution greater than 6.