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Find the value of $\sqrt[3]{216}-\sqrt[3]{125}$.

Last updated date: 22nd Jul 2024
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Hint: For solving this question you should know about how to calculate the cube root of any number. In this problem we will find the cube roots of the given terms and then we will solve this directly as desired. Thus we will get the answer.

Complete step by step answer:
According to our question, we have been asked to find the value of $\sqrt[3]{216}-\sqrt[3]{125}$. For finding the cube root of any number we use many methods and we can also solve the cube root of any number by long division method also. And it is useful for finding the cube roots for non-perfect cube numbers.
As we know for solving using the long division method, we use just simple steps as follows:
Step 1: Divide our given term by which it is asked and it will be a simple division.
Step 2: Now we will multiply the quotient with the divider and put the value of that at the subtraction of the first digit.
Step 3: Then we put the remaining single digit with the result of this subtraction and then we get it as a new number.
Step 4: Now we get a new number. Apply the same above steps with it and finally get the last remainder which can’t be divisible by anything else or we get a remainder as 0.
Step 5: If you want to check this, then you can do so with the formula:
Dividend = Divisor $\times $ Quotient + Remainder
According to our question,
$\sqrt[3]{216}-\sqrt[3]{125}=\sqrt[3]{6\times 6\times 6}-\sqrt[3]{5\times 5\times 5}$
It is a perfect cube formed, so these can be solved directly as,
So, the answer is 1.

Note: While solving this question or all other related questions to the long division method, always try to make it fully divided or make the remainder zero. And if the question is asked for the square root, then it is mandatory for the remainder to be zero. If this will be zero, then maybe your calculations are wrong and you will never get the solution right.