Question

Find the cube root of the following integer −753571.

Answer 1

We have:

\[\sqrt[3]{- 753571} = - \sqrt[3]{753571}\]

To find the cube root of 753571, we use the method of unit digits.

Let us consider the number 753571.
The unit digit is 1; therefore the unit digit in the cube root of 753571 will be 1.
After striking out the units, tens and hundreds digits of the given number, we are left with 753.
Now, 9 is the largest number whose cube is less than or equal to 753 (\[9^3 < 753 < {10}^3\]).

Therefore, the tens digit of the cube root 753571 is 9.

∴ \[\sqrt[3]{753571} = 91\]

⇒ \[\sqrt[3]{- 753571} = - \sqrt[3]{753571} = - 91\]