Question

What is ${{\left( \dfrac{1}{2} \right)}^{2}}$?

Answer 1

Hint: The above given question is in fraction form. Here we have to find the square root of fractions. Normally we had been studying only the squares of natural numbers and integers. A fraction represents a part of a whole or, more generally, any number of equal parts. The fraction has two parts. One part is a numerator and the second part is a denominator. The upper part of the fraction is called numerator and lower part is called denominator.

Complete step by step solution:
Here the given question is:
$\Rightarrow {{\left( \dfrac{1}{2} \right)}^{2}}$
Since we can also see the above question is looking like a rational number too, because we know in the rational number the denominator part of the above question is non zero. Since we have been studying how to find the square of any natural number and integer. What we do if we have any random number a and if we have to find a square then we simply multiply the a two times or we can say ${{a}^{2}}=a\times a$.
But here we have numbers in a fraction form so we will use the other formula. If we have any fraction like $\dfrac{a}{b}$ and here if we have to find the square of the this fraction then we will use ${{\left( \dfrac{a}{b} \right)}^{2}}=\dfrac{{{a}^{2}}}{{{b}^{2}}}$
Here we have ${{\left( \dfrac{1}{2} \right)}^{2}}$ so by using above formula, we get
$\Rightarrow {{\left( \dfrac{1}{2} \right)}^{2}}=\dfrac{{{1}^{2}}}{{{2}^{2}}}=\dfrac{1}{4}$
Hence we get the square of $\dfrac{1}{2}$is $\dfrac{1}{4}$.

Note: It is not hard to find the square of the fraction, but the only thing that matters is that we have to know the basic operation of mathematics which is always used to find the square is multiplication. We know If we have any random number a and if we have to find square then we simply multiply the a two times or we can say ${{a}^{2}}=a\times a$.The square of ${{\left( \dfrac{1}{2} \right)}^{2}}=\dfrac{1}{2}\times \dfrac{1}{2}$ , so if we multiply numerator terms and denominator term we get $\dfrac{1\times 1}{2\times 2}=\dfrac{1}{4}$.