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
-
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 $x^3 = 45$.
-
Rewrite the equation We can express this in a more useful form for calculation: $$ x = \sqrt[3]{45} $$
-
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.
-
Use a calculator or approximations To find a more precise value for $x$, we can use a calculator or estimate further. Using a calculator: $$ x \approx 3.571 $$
-
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.
