Question

Check whether 1152 is a perfect square. If not, find the nearest number by which it should be divided so that the quotient becomes a perfect square. Also, find the square root of the quotient.
A) 2, 24
B) 3, 24
C) 2, 19
D) 3, 19

Answer 1

Hint:
Firstly, we will check if the given number is a perfect square or not.
Then will factories the given number.
Then after will multiply the given number with the number which is not paired after factories.

Complete step by step solution:
We have to check whether 1152 is a perfect square or not.
If it is not the perfect square then we have to find the nearest number by which it should be divided
$ \Rightarrow 1152 = $${2^2} \times {2^2} \times {2^2} \times 2 \times {3^2}$
All the numbers paired except the prime factor 2.
Now, we should divide 1152 by 2
\[1152 \div 2{\text{ }} = {\text{ }}576\]
Thus, the required least number is 2

$\therefore $ The square root of the quotient is$\sqrt {576} = 24$

Note:
Perfect Square: Perfect square or a square number is an integer that is a square of an integer. In other words, it is the product of some integer with itself.
For example,
$
  {4^2} = 4 \times 4 = 16 \\
  {8^2} = 8 \times 8 = 64 \\
  {10^2} = 10 \times 10 = 100 \\
  $