Question

Is $\dfrac{1}{4}$ a perfect square?

Answer 1

Hint: Perfect square can be defined as the number that can be made by squaring a whole number or it can be defined as if a natural number is multiplied by itself. Here, we have to find that $\dfrac{1}{4}$ is a perfect square or not. The number is called the perfect square perfect square, when we apply the square root to the number. Square and square root are inverse to each other.

Complete step by step answer:
Here we have to find that $\dfrac{1}{4}$ is a perfect square
Here the given number is in fraction. Fraction is a number which comes under the rational number, the rational number is represented in the form of $\dfrac{p}{q}$ where $q \ne 0$. Fractions are of three kinds namely, proper fraction, improper fraction and mixed fraction. If the fraction is a mixed fraction, first convert it into an improper fraction.
For the fraction to be a perfect square both numerator and denominator have to be a perfect square.
So we now apply the square root to the given fraction $\dfrac{1}{4}$. The square root is to be implied on both the numerator and denominator.
The square and the square root are inversely related to each other. The number is called the perfect square, when we apply the square root to the number if we obtain the number which is not in fraction and decimal.
So, we have $\sqrt 1 = 1$ and $\sqrt 4 = 2$
Both numerator and denominator are perfect squares.
So, we can write $\dfrac{1}{4}$ as
$\sqrt {\dfrac{1}{4}} = \dfrac{1}{2}$
Hence, $\dfrac{1}{4}$ is a perfect square.

Note:
For solving such kinds of problems the division method and the tables of multiplication are very important. Note that squares of even numbers result in even numbers and squares of odd numbers always result in odd numbers. For fractions to be perfect both numerator and denominator should be a perfect square.