Question

The square root of 81% is
A.8%
B.0.9
C.0.9%
D.20

Answer 1

Hint: We recall the concept of percentage and square root. We convert the given percentage into fraction $p\mathrm{\%}={\displaystyle \frac{p}{100}}$ and then take the square root on the numerator to denominator to find the square root of the fraction. We convert the square root into decimals and choose the correct option.

Complete step by step answer:
We know that percentage is derived from the word per centum in Latin which means per hundred. The percentage in mathematics is a number or ratio expressed as a fraction of 100. When we say $p$% it means, ${\displaystyle \frac{p}{100}}$.
We know that the square root of a number $n$ is a number with whom by multiplying itself we get the number $n$. The square root of $n$ is represented as $\sqrt{n}$.
We know that we can find square root of a rational number ${\displaystyle \frac{a}{b}},a\ge 0,b>0$ using the working rule;
$$\sqrt{{\displaystyle \frac{a}{b}}}={\displaystyle \frac{\sqrt{a}}{\sqrt{b}}}$$
We are asked in the question to find the square root 81%. We use the definition of percentage and have
$$81\mathrm{\%}={\displaystyle \frac{81}{100}}$$
Let us take square root both side of the above equation and have;
$$\sqrt{81\mathrm{\%}}=\sqrt{{\displaystyle \frac{81}{100}}}$$
We use the working rule of finding square root of rational number and have;
$$\Rightarrow \sqrt{81\mathrm{\%}}={\displaystyle \frac{\sqrt{81}}{\sqrt{100}}}$$
We find the square root of 81 as 9 since $9\times 9=81$ and the square root of 100 as 10 since $10\times 10=100$. We have;
$$\Rightarrow \sqrt{81\mathrm{\%}}={\displaystyle \frac{9}{10}}$$
We convert the fraction into decimal in the above equation and have;
$$\Rightarrow \sqrt{81\mathrm{\%}}=0.9$$

So, the correct answer is “Option B”.

Note: We must be careful that the square root of percentage is not a percentage. We are given in the option value 0.9% which we can convert to decimal as ${\displaystyle \frac{0.9}{100}}={\displaystyle \frac{9}{1000}}$. We must note that when we say square root, it always means positive square root unless we are solving equations. We can directly find the square root of $81\mathrm{\%}=0.81$ if we know the decimal multiplication.