Question

Find the cube root of 175616.
A. 56
B. 46
C. 66
D. 76

Answer 1

Hint: We have to find the cube root of 175616. So, first of all we have to understand the basic rule of cube root of any number that is mentioned below.
Cube root: The cube root of any number is the factor of that number three times to get its cube, so in this case, we break down a number to be expressed as a product of three equal numbers and thus we get the cube root. So we can say, the cube root gives the value which is basically three times of itself or cubed.

Complete step-by-step solution:
Step 1: First of all we have to determine the factors of 175616 by dividing with 2 as,
$ \Rightarrow 2 \times 2 \times 2 \times 21952 = 175616$
Step 2: Now, same as the step 1 we have to determine the factors of 21952 by dividing it by 2 again hence,
$ \Rightarrow 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2744 = 175616$
Step 3: Now, same as the step 1 we have to determine the factors of 2744 by dividing it by 2 again hence,
$ \Rightarrow 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 343 = 175616$
Step 4: Now, same as the step 1 we have to determine the factors of 343 by dividing it by 7 again hence,
$ \Rightarrow 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7 = 175616$
Now, we have to make the three pairs of factors obtained in step 4 after taking cube root. We get:
$
   \Rightarrow \sqrt[3]{{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7}} \\
   \Rightarrow 2 \times 2 \times 2 \times 7 \\
   \Rightarrow 56
 $
Final solution: The cube to the number 175616 is 56.

So, the option (A) is correct.

Note: To find the cube root of 175616 first of all we have to divide the given number by 2 until it’s not divisible by 2 then we have to check if it is divisible by 3, 5, 6, or 7.
The cube root of any number is the factor of that number three times to get its cube, so in this case, we break down a number to be expressed as a product of three equal numbers and thus we get the cube root.