Question

State whether true or false: A perfect cube does not end with two zeros.
A . True
B . False

Answer 1

Hint: Use the concept that the cube of number ending with zero will have the number that is ending with three zeroes. Also, check if there is any number if there is any number whose cubes is ending with two zeroes.

Complete step-by-step answer:
In the question, we have to check if the statement which says that a perfect cube does not end with two zeros is correct or not. So here we will start with the number ending with 1, then its cube will also end with 1, as shown below:
\[{{1}^{3}}=1\]
Next, we will take a number ending with 2, we will take the cube of this number and we will get the number ending with 8, as shown below:
\[{{2}^{3}}=8\]
Next, we will take a number ending with 3, we will take the cube of this number and we will get the number ending with 8, as shown below:
\[{{3}^{3}}=27\]
Next, we will take a number ending with 4, we will take the cube of this number and we will get the number ending with 4, as shown below:
\[{{4}^{3}}=64\]
Next, we will take a number ending with 5, we will take the cube of this number and we will get the number ending with 5, as shown below:
\[{{5}^{3}}=125\]
Next, we will take a number ending with 6, we will take the cube of this number and we will get the number ending with 6, as shown below:
\[{{6}^{3}}=216\]
Next, we will take a number ending with 7, we will take the cube of this number and we will get the number ending with 3, as shown below:
\[{{7}^{3}}=343\]
Next, we will take a number ending with 8, we will take the cube of this number and we will get the number ending with 2, as shown below:
\[{{8}^{3}}=512\]
Next, we will take a number ending with 9, we will take the cube of this number and we will get the number ending with 9, as shown below:
\[{{9}^{3}}=729\]
Next, we will take a number ending with 0, we will take the cube of this number and we will get the number ending with three zeroes, as shown below:
\[{{10}^{3}}=1000\]
So, in no case we get a number whose cube ends with two zeroes. Hence, the statement which says that: A perfect cube does not end with two zeros, is true.
Hence, the correct answer is option A.

Note: One method to do this problem is find the cube root of the number ending with two zeroes, then we will never get a perfect integer number, instead we will always get a decimal number. For example: \[\sqrt[3]{900}=9.65\]. So, from this we can say that the statement, perfect cube does not end with two zeros, is true.