Question

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\sqrt[3]{4}$$

Short answer

The approximate cube root of 4 rounded to two decimal places is 1.59.

Step-by-step solution

Identify the radical

Recognize that the given radical is \(\root[3]{4}\), which means the cube root of 4.

Use a calculator to find the cube root

Enter 4 into your calculator and use the cube root function (often labeled as \( \root[3]{x} \)). If your calculator does not have a cube root function, you can raise 4 to the power of \(1/3\).

Perform the calculation

Using the calculator, \( \root[3]{4} \) is approximately 1.5874.

Round the answer

Round 1.5874 to two decimal places. The result is 1.59.

Key concepts

cube root

Calculating the cube root of a number means finding a value that, when multiplied by itself three times, gives the original number. For instance, the cube root of 4 is a number that, when cubed, equals 4. The cube root of 4 is denoted as \(\root[3]{4}\). This may seem tricky at first, but with practice, it becomes easier.
Understanding cube roots helps in solving various mathematical problems, especially those dealing with volumes and geometry.

radical approximation

Radical approximation involves finding an approximate value for a radical expression when an exact answer is not easy to obtain manually. The radical in our problem is \(\root[3]{4}\). To approximate this, we use tools such as calculators or estimation techniques.
For cube roots, most common calculators have a special function. If not, you can always raise the number to the power of \( \frac{1}{3} \). This method gives you a close approximation of the cube root value.

calculator usage

Using a calculator is straightforward when it comes to finding cube roots. Simply enter the number whose cube root you need, and use the cube root function often labeled as \(\root[3]{x}\).
If your calculator lacks this function, you can still find cube roots by raising the number to the power of \(1/3\). For example, \(\root[3]{4}\) means you input \(4^{1/3}\) into your calculator. This will yield an approximate value.
It's important to familiarize yourself with your calculator’s functions. Reviewing your manual or exploring the calculator’s menu can be very helpful.

rounding numbers

Rounding numbers is the process of reducing the number of digits right of the decimal while keeping the value close to what it was. When you have a decimal like 1.5874 from \(\root[3]{4}\), rounding to two decimal places means focusing on only the first two digits after the decimal point.
Check the third digit: if it's 5 or greater, round up the second digit; if it's less than 5, leave the second digit as it is. In this example, 1.5874 rounds to 1.59 because the third digit (7) is greater than 5. Regular practice with rounding will make this process intuitive.