Question

Find the cube root of the following number −27 × 2744 .

Answer 1

Property:
For any two integers a and b,

\[\sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b}\]

\[\sqrt[3]{- 27 \times 2744}\]

\[ = \sqrt[3]{- 27} \times \sqrt[3]{2744}\]

\[= - \sqrt[3]{27} \times \sqrt[3]{2744}\]     (For any positive integer x,

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

Cube root using units digit:
Let us consider the number 2744.
The unit digit is 4; therefore, the unit digit in the cube root of 2744 will be 4.
After striking out the units, tens, and hundreds digits of the given number, we are left with 2.
Now, 1 is the largest number whose cube is less than or equal to 2.
Therefore, the tens digit of the cube root of 2744 is 1.

∴ \[\sqrt[3]{2744} = 14\]

Thus

\[\sqrt[3]{- 27 \times 2744} = - \sqrt[3]{27} \times \sqrt[3]{2744} = - 3 \times 14 = - 42\]