Question

The numbers that end in 2, 3, 7 or 8 are called ________ squared numbers.
A. perfect
B. non-perfect
C. rational
D. real

Answer 1

Hint: Write the square of a number from 1 to 10 and observe its units place carefully and also check whether it is a perfect square or non-perfect square number.

Complete step-by-step answer:
We have been asked to find what the numbers that end in 2, 3, 7 or 8 are known as. In the question, after the blank to be filled, we have the word “squared”, so it means that we have to find the answer with respect to the square of numbers.
So, let us consider numbers from 1 to 10 and then write the square of each number from 1 to 10. Then, we get,
\[\begin{align}
  & {{1}^{2}}=1 \\
 & {{2}^{2}}=4 \\
 & {{3}^{2}}=9 \\
 & {{4}^{2}}=16 \\
 & {{5}^{2}}=25 \\
 & {{6}^{2}}=36 \\
 & {{7}^{2}}=49 \\
 & {{8}^{2}}=64 \\
 & {{9}^{2}}=81 \\
 & {{10}^{2}}=100 \\
\end{align}\]
We can observe that the number ends in 0, 1, 4, 9, 6 and 5 and all are perfect square numbers which means the square root of the number is an integer.
Also, the number that ends in 2, 3, 7 or 8 like 12, 13, 17 or 18 etc. are all non-perfect square numbers which means that the square root of the number is not an integer.
Therefore, the correct option of the above question is option B.

Note: Be careful while choosing the option as you can think that the number that ends in 2, 3, 7 or 8 can be a rational or real number but we have been asked for perfect and non-perfect square numbers only.