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Question
Find the cube root of the following integer −5832 .
Solution
We have:
\[\sqrt[3]{- 5832} = - \sqrt[3]{5832}\]
To find the cube root of 5832, we use the method of unit digits.
Let us consider the number 5832.
The unit digit is 2; therefore the unit digit in the cube root of 5832 will be 8.
After striking out the units, tens and hundreds digits of the given number, we are left with 5.
Now, 1 is the largest number whose cube is less than or equal to 5.
Therefore, the tens digit of the cube root of 5832 is 1.
∴ \[\sqrt[3]{5832} = 18\]
⇒ \[\sqrt[3]{- 5832} = - \sqrt[3]{5832} = - 18\]
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