x*x*x is equal to 2: Correct answer explained

Question: If x*x*x is equal to 2, what is the value of x? The original item does not provide clear multiple-choice options. The visible given answer says x = √2, but that does not match the equation x*x*x = 2.

The correct answer is x = ∛2. Since x*x*x means x multiplied by itself three times, the equation is x³ = 2. To undo “cubing,” take the cube root of both sides, so x = ∛2.

Why x = ∛2 is the correct value

x*x*x is the same as x³, read as “x cubed.” So the equation x*x*x = 2 becomes x³ = 2. The number that makes this true is the cube root of 2, written as ∛2.

A cube root asks: “What number, multiplied by itself three times, gives this result?” For example, ∛8 = 2 because 2 × 2 × 2 = 8. In the same way, ∛2 is the number that gives 2 when multiplied by itself three times.

As a decimal, ∛2 is about 1.26, because 1.26 × 1.26 × 1.26 is close to 2. The exact answer is still ∛2, because the decimal form continues and is not as clean as the radical form.

Why the other visible answer is not correct

√2 is not correct for x*x*x = 2. The square root of 2 answers a different question: “What number multiplied by itself two times gives 2?” That means √2 × √2 = 2, not √2 × √2 × √2 = 2.

This is the easiest mistake to make. Square root connects to x², while cube root connects to x³. Since the equation has three x’s multiplied together, the answer must use a cube root, not a square root.

The value x = 2 is also not correct for this equation. If x = 2, then x*x*x = 2 × 2 × 2 = 8, not 2.

Important note about the original image

The image alt text shows x^(x^x)=2, which is a different equation from x*x*x = 2. These two equations should not be treated as the same problem.

For x*x*x = 2, the answer is ∛2. For x^(x^x)=2, the solution is not found by simply taking a cube root, and the visible answer √2 is not supported by the basic substitution check.

Quick way to recognize this type of question

Count how many times x is multiplied by itself. If there are two x’s, use a square root. If there are three x’s, use a cube root.

So the shortcut is simple: x*x*x is equal to 2 means x³ = 2, and x = ∛2. Do not choose √2 unless the equation is x*x = 2.