What is the cube root of 45?

Understand the Problem

The question asks for the cube root of 45, which means we need to find a number that, when multiplied by itself three times, equals 45. This is a mathematical problem that requires a step-by-step calculation.

Answer

The cube root of 45 is approximately $3.571$.
Answer for screen readers

The cube root of 45 is approximately $x \approx 3.571$.

Steps to Solve

  1. Set up the equation for the cube root To find the cube root of 45, we denote it as $x$. This means we are looking for $x$ such that $x^3 = 45$.

  2. Rewrite the equation We can express this in a more useful form for calculation: $$ x = \sqrt[3]{45} $$

  3. Estimate the cube root of 45 Since we know that $3^3 = 27$ and $4^3 = 64$, we know that the cube root of 45 is between 3 and 4.

  4. Use a calculator or approximations To find a more precise value for $x$, we can use a calculator or estimate further. Using a calculator: $$ x \approx 3.571 $$

  5. Verification To ensure that our answer is correct, we can cube our result: $$ (3.571)^3 \approx 45 $$

The cube root of 45 is approximately $x \approx 3.571$.

More Information

The cube root represents a number that, when multiplied by itself three times, gives you the original value. The cube root is often used in various fields of science and engineering.

Tips

  • Mistaking the cube root for the square root. Remember, cube roots involve multiplying the number by itself three times, not two.
  • Rounding too early. It's important to keep track of decimal places until the final answer is calculated.
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