Find the cube root of 81: root(81, 3) (1 point)
9
27
root(81, 3)
-9
The cube root of 81 is 4.3267487109222245.
To find the cube root of 81, we can use the formula:
\[ \sqrt[3]{81} \]
Calculating the cube root of 81, we get:
\[ \sqrt[3]{81} = 4.3267487109222245 \]
So, the cube root of 81 is approximately 4.3267487109222245.
To find the cube root of 81, we can use the formula:
\[ \sqrt[3]{81} \]
There are a few ways to calculate the cube root.
Method 1: Using a Calculator
Many calculators have a cube root function. Simply enter 81 and find the cube root function (often denoted by a radical symbol with a 3 as the index). Pressing the equals button will give you the cube root of 81.
Method 2: Repeated Multiplication (Approximation)
One method to approximate the cube root of 81 is to repeatedly multiply a number by itself until the cube of that number is close to 81. For example, let's start with 2:
\( 2 \times 2 \times 2 = 8 \) (not close enough to 81)
Now let's try 3:
\( 3 \times 3 \times 3 = 27 \) (still not quite large enough)
Finally, let's try 4:
\( 4 \times 4 \times 4 = 64 \) (too small)
We can see that the cube root must be between 3 and 4. To get a closer approximation, we can divide the difference between 81 and the cube of 3 (27) by the sum of the cube of 4 (64) and the cube of 3 (27):
\( \left( \frac{81 - 27}{64 + 27} \right) \times 1 \)
\( \left( \frac{54}{91} \right) \times 1 \)
\( \approx 0.59340 \)
By adding this approximation to the original estimate of 3, we obtain a more accurate value:
\( 3 + 0.59340 \approx 3.59 \)
So, the approximate value of the cube root of 81 is 3.59.
Method 3: Using Exponentiation
Another method to find the cube root is to use exponentiation. We can rewrite \( \sqrt[3]{81} \) as \( 81^{1/3} \). By raising 81 to the power of 1/3, we can calculate the cube root.
\( 81^{1/3} \approx 4.32674871092222 \)
So, the approximate value of the cube root of 81 is 4.32674871092222.
In the given options, the correct answer is 4.