Find the cube root of 81 ³√81
The cube root of 81 is written as ³√81 or ∛81.
To find this value, we need to find the number that, when multiplied by itself twice (cubed), equals 81.
Let's start by guessing numbers and cubing them:
1³ = 1
2³ = 2 x 2 x 2 = 8
3³ = 3 x 3 x 3 = 27
4³ = 4 x 4 x 4 = 64
5³ = 5 x 5 x 5 = 125
From this, we can see that 4³ is the largest value that is still less than 81. Therefore, the cube root of 81 is 4.
To find the cube root of 81, you can follow these steps:
Step 1: Start with the number 81.
Step 2: Find the prime factorization of 81.
The prime factorization of 81 is 3 × 3 × 3 × 3.
Step 3: Group the prime factors into pairs of three.
(3 × 3) × (3 × 3) = 9 × 9
Step 4: Take the cube root of each pair of threes.
∛(9 × 9) = 9
Therefore, the cube root of 81 is 9.
To find the cube root of a number, we need to determine the number that, when raised to the power of 3, equals the original number. In this case, we want to find the cube root of 81.
To solve this, we can use a calculator or perform the calculation manually. Let's use the manual method:
To find the cube root of 81, we need to determine a number that, when raised to the power of 3, equals 81.
Start by testing different numbers:
- Choose a number, let's say 3, and raise it to the power of 3: 3³ = 27 (not equal to 81)
- Try again with another number, let's say 4: 4³ = 64 (still not equal to 81)
- Continue with different numbers until you find the cube root.
Now, you might notice that 3 is too small and 4 is too large. To narrow down the range, we can use a technique called "estimation" to find the approximate value.
Since the cube root of 81 lies between 3 and 4, we can estimate a value for the cube root. Let's try 3.5 as an estimate.
Now, let's calculate the cube of 3.5:
3.5³ = 3.5 × 3.5 × 3.5 = 42.875
As 42.875 is less than 81, our estimate was too small. We could now try a larger estimate. However, for this particular example, we can see that the next whole number, 4, is likely to be the cube root, as it is only one unit away from the estimated value of 3.5.
Let's calculate the cube of 4:
4³ = 4 × 4 × 4 = 64
Since 64 is less than 81, we know that our estimate was too small. By the same logic, any number smaller than 4 would also yield a cube smaller than 81.
Therefore, we can conclude that the cube root of 81 is 4.
Alternatively, you can use a calculator or a mathematical software to find the cube root of 81 instantly.