Question

Find the cube root of the following integer −32768 .

Answer 1

We have: \[\sqrt[3]{- 32768} = - \sqrt[3]{32768}\]

To find the cube root of 32768, we use the method of unit digits.

Let us consider the number 32768.
The unit digit is 8; therefore, the unit digit in the cube root of 32768 will be 2.
After striking out the units, tens and hundreds digits of the given number, we are left with 32.
Now, 3 is the largest number whose cube is less than or equal to 32 (\[3^3 < 32 < 4^3\]).

Therefore, the tens digit of the cube root 32768 is 3.

∴ \[\sqrt[3]{32768} = 32\]

⇒ \[\sqrt[3]{- 32768} = - \sqrt[3]{32768} = - 32\]