The digit in the units place in the cube root of 21952 is

Options

A. 8
B. 6
C. 4
D. 2

Answer

To find the digit in the units place of the cube root of 21952, we can follow these steps:

### Step 1: Prime Factorization of 21952
We start by breaking down 21952 into its prime factors. We can do this using the method of successive division.

1. Divide by 2:
- 21952 ÷ 2 = 10976
2. Divide by 2 again:
- 10976 ÷ 2 = 5488
3. Divide by 2 again:
- 5488 ÷ 2 = 2744
4. Divide by 2 again:
- 2744 ÷ 2 = 1372
5. Divide by 2 again:
- 1372 ÷ 2 = 686
6. Divide by 2 again:
- 686 ÷ 2 = 343
7. Now 343 is not divisible by 2, so we try the next prime number, which is 7:
- 343 ÷ 7 = 49
8. Divide by 7 again:
- 49 ÷ 7 = 7
9. Finally, divide by 7:
- 7 ÷ 7 = 1

So, the prime factorization of 21952 is:
\[ 21952 = 2^6 \times 7^3 \]

### Step 2: Group the Factors for Cube Root
Next, we can group the factors to find the cube root. Since we are looking for the cube root, we can group the factors in sets of three.

- From \(2^6\), we can take out \(2^2\) (since \(2^6 = (2^2)^3\)).
- From \(7^3\), we can take out \(7\) (since \(7^3 = 7^1\)).

Thus, we can express 21952 as:
\[ 21952 = (2^2)^3 \times (7^1)^3 \]

### Step 3: Calculate the Cube Root
Now we can calculate the cube root:
\[ \sqrt[3]{21952} = \sqrt[3]{(2^2)^3 \times (7^1)^3} \]
\[ = 2^2 \times 7 = 4 \times 7 = 28 \]

### Step 4: Find the Units Place
The last step is to find the digit in the units place of the number we calculated:
- The units place of 28 is **8**.

### Final Answer
The digit in the units place in the cube root of 21952 is **8**.

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