Question

Square root of 81% is?
(a)8%
(b)0.9
 (c) 0.9%
(d)20

Answer 1

Hint: If a fraction $\dfrac{a}{b}$ is given to us we can calculate the percentage by just multiplying $\dfrac{a}{b}$with 100. Whenever we are given $c%$, it translates into $\dfrac{c}{100}$. If a fraction $\dfrac{a}{b}$ on conversion to percentage is c% , then $\dfrac{a}{b}=\dfrac{c}{100}$.

Complete step by step answer:
Therefore, $81%=\dfrac{81}{100}$. Thus, to find the square root of 81% we have to find the square root of $\dfrac{81}{100}$.

Now, $\sqrt{\dfrac{81}{100}}=\sqrt{\dfrac{9\times 9}{10\times 10}}=\sqrt{\dfrac{{{9}^{2}}}{{{10}^{2}}}}=\sqrt{{{\left( \dfrac{9}{10} \right)}^{2}}}$

Since, the square of $\dfrac{9}{10}$ is $\dfrac{81}{100}$. Therefore, the square root of $\dfrac{81}{100}$ is $\dfrac{9}{10}$.

Now $\dfrac{9}{10}$ can further be converted into decimal. In decimal form, $\dfrac{9}{10}$is equivalent to 0.9 .

Note: We can understand the concept of percentage by following example:
Suppose you have a bar of chocolate and your father asks you to give $\dfrac{3}{4}$of the chocolate to your younger sister and one of your naughty elder brothers cuts your chocolate into 100 equal pieces. Now, out of 100 pieces how many will you give to your younger sister so that she gets exactly $\dfrac{3}{4}$ of the original chocolate bar?
Since the chocolate bar is divided into 100 equal pieces if you give ${{\left( \dfrac{3}{4} \right)}^{th}}$of 100 pieces then your sister will get $\dfrac{3}{4}$of the whole chocolate bar.
Now, $\dfrac{3}{4}\times 100=75$. Therefore, your sister should get 75 pieces out of 100 pieces. This is the same as saying that you have given 75% of your chocolate to your sister.