Question

What is the least number which must be subtracted from $369$ to make it a perfect cube?
$A)8$
$B)26$
$C)2$
$D)25$

Answer 1

Hint: Since we just need to know such things about the square root numbers and perfect square numbers, A perfect square is the numbers that obtain by multiplying any whole numbers (zero to infinity) twice, or the square of the given numbers yields a whole number like $\sqrt {25} = 5$or $25 = {5^2}$
Similarly, the perfect cube can be expressed as $\sqrt[3]{3} = 27,27 = {3^3}$

Complete step by step answer:
Since from the given that we have the number $369$ and we need to make this as a perfect cube number with some other number will be subtracted.
Hence, we need to find the unknown number which will be subtracted to make the given number as a perfect cube. So, we will go according to the options.
$A)8$ let us see if we subtract the given number by this we get $369 - 8 = 361$ which is not the perfect cube.
Since the basic perfect cube numbers as ${1^3} = 1,{2^3} = 8,{3^3} = 27,{4^3} = 64,{5^3} = 125,{6^3} = 216,{7^3} = 343,{8^3} = 512$
Hence the option $A)8$ is wrong.
$C)2$ let us see if we subtract the given number by this we get $369 - 2 = 367$ which is not the perfect cube.
Since the basic perfect cube numbers as ${1^3} = 1,{2^3} = 8,{3^3} = 27,{4^3} = 64,{5^3} = 125,{6^3} = 216,{7^3} = 343,{8^3} = 512$
Hence the option $C)2$ is wrong.
$D)25$ let us see if we subtract the given number by this we get $369 - 25 = 344$ which is not the perfect cube.
Since the basic perfect cube numbers as ${1^3} = 1,{2^3} = 8,{3^3} = 27,{4^3} = 64,{5^3} = 125,{6^3} = 216,{7^3} = 343,{8^3} = 512$
Hence the option $D)25$ is wrong.
$B)26$ let us see if we subtract the given number by this we get $369 - 26 = 343$ which is not the perfect cube.
Since the basic perfect cube numbers as ${1^3} = 1,{2^3} = 8,{3^3} = 27,{4^3} = 64,{5^3} = 125,{6^3} = 216,{7^3} = 343,{8^3} = 512$
Hence which is the perfect cube because $343 = {7^3}$ and hence we get $B)26$ is correct
Thus $26$ is the least number which must be subtracted from $369$ to make it a perfect cube.

So, the correct answer is “Option B”.

Note:
Since we are asked for the least number, after the number $7$ cube the numbers are exceeding the given values and thus we need to stop the process on the cube $7$. Because the $8$ cube will be a larger number.
Hence the least number can be calculated using the trial and error method, we just apply the given values and then we get the answer that we require.