Question

The Number mentioned below is a perfect square 222000.
1) True
2) False

Answer 1

Hint:
Here, we will find whether the given number is a perfect square or not. We will find the square root of a number by the method of prime factorization. A number multiplied by itself is known as a square number or perfect square.

Complete step by step solution:
We will find the square root of the number 222000.
The square root of the number can be found by using the method of prime factorization.
$\begin{array}{*{20}{l}}
  2 | {222000} \\
\hline
  2 | {111000} \\
\hline
  2 | {55500} \\
\hline
  2 | {27750} \\
\hline
  3 | {13875} \\
\hline
  5 | {4625} \\
\hline
  5 | {925} \\
\hline
  5 | {185} \\
\hline
  {37} | {37} \\
\hline
  {} | 1
\end{array}$
Thus, the factor of 222000 is $2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 37$.
$\sqrt {222000} = \sqrt {2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 37} $
The factors 3,5 and 37 are not expressed in pairs, so the given number is not a perfect square.
Thus, 222000 is not a perfect square.
Therefore, the number mentioned below is not a perfect square 222000 i.e., false.

Thus, option (B) is the correct answer.

Note:
We need to know the rules for a number to be a perfect square. If the unit digit is 1, 4, 5, 6, 9 and 0, then the number must be a perfect square. If the unit digit is 5, then its ten’s digit is always 2. If the unit digit is 6, then its tens digit is always odd. If the unit digit is 1, 4, 5, 9, 0, then the tens digit is always even. We can also check by leaving the zeroes at the last, and considering the last digit of a number except zero, then we will find the perfect square or not by the rules. Therefore, 222000 is not a perfect square, since it has an odd number of zeroes.