Question

: The number of perfect squares between 1 to 100 natural numbers.
A) 6
B) 7
C) 8
D) 9

Answer 1

Hint:
Write the square root of the natural numbers from 1 to 100, which have a perfect square. Count the numbers that are perfect squares. Include the numbers that lie between 1 to 100. Do not include 1 and 100 while counting the numbers of perfect squares between 1 and 100.

Complete step by step solution:
The perfect squares are the square of whole numbers.
We will first write the square root of the natural numbers from 1 to 100, which have a perfect square.
$
  \sqrt 1 = 1 \\
  \sqrt 4 = 2 \\
  \sqrt 9 = 3 \\
  \sqrt {16} = 4 \\
  \sqrt {25} = 5 \\
  \sqrt {36} = 6 \\
  \sqrt {49} = 7 \\
  \sqrt {64} = 8 \\
  \sqrt {81} = 9 \\
  \sqrt {100} = 10 \\
$
We can see that, there are 10 perfect squares from 1 to 10.
But, there are only 8 square roots between 1 to 10 after excluding 1 and 10.

Therefore, the number of perfect squares between 1 to 100 natural numbers is 9.
Hence, option D is correct.

Note:
Perfect squares are the numbers which we obtain by multiplying any whole number twice . Many students make mistakes by including 1 and 10, but in this question it is mentioned that we have to find the numbers in between 1 and 100, therefore, we need to exclude 1 and 10.