
Find the cube root of a given number through estimation:
Answer
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Hint: Start with finding the unit digit of the given number by using the property that says that the unit digit of the product of numbers is the same as the unit digit of the product of the unit digits of the numbers. After finding the unit digit, find the tens multiple between which the required number lies, i.e. .
Complete step-by-step answer:
Here in this problem, we are given a positive integer . We need to find out the cube root of this number through estimation without performing a long calculation.
As we know that the unit digit of the product of two numbers is the same as the unit digit of the product of the unit digits of the two numbers, i.e.
Considering two numbers where ‘a’, ‘b’, ‘c’, ‘d’, ‘w’, ‘x’, ‘y’ and ‘z’ are the digits of these two given numbers.
Unit digit of Unit digit of
If we consider the given number to be the cube of a number ‘m’, then
Then from the above relation, we can say:
Unit digit of Unit digit of
As we know that the only single-digit number which has as the unit digit of its cube is
Therefore, we can conclude that the unit digit of the required number ‘m’ is
Now we can find the number between which the given cube number will lie.
As we know and
But the given number lies between
Thus, we came up to the conclusion that the unit digit of the cube root of is and the cube root of lies between and .
Therefore, the required cube root of the required number can only be .
.
Note: In questions like this, knowing the nearest cubes of the number or finding the cubes of multiples of ten always plays an important role. The cubes or squares of multiples of tens can be easily found by simply multiplying the non-zero together then placing the same number of zeroes from the right. For example, .
Complete step-by-step answer:
Here in this problem, we are given a positive integer
As we know that the unit digit of the product of two numbers is the same as the unit digit of the product of the unit digits of the two numbers, i.e.
Considering two numbers
If we consider the given number to be the cube of a number ‘m’, then
Then from the above relation, we can say:
As we know that the only single-digit number which has
Therefore, we can conclude that the unit digit of the required number ‘m’ is
Now we can find the number between which the given cube number will lie.
As we know
But the given number lies between
Thus, we came up to the conclusion that the unit digit of the cube root of
Therefore, the required cube root of the required number can only be
Note: In questions like this, knowing the nearest cubes of the number or finding the cubes of multiples of ten always plays an important role. The cubes or squares of multiples of tens can be easily found by simply multiplying the non-zero together then placing the same number of zeroes from the right. For example,
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