 QUESTION

# Find the square root of 12.25a)3.5b)4.25c)4.5d)3

Hint: In this question, we have to find the square root of a decimal number. Thus, we can try to express it in the form of the expansion of a sum of numbers i.e. in the form of ${{a}^{2}}+{{b}^{2}}+2ab$ which by the square of a sum rule would be same as ${{\left( a+b \right)}^{2}}$. Thus, in this way, we can express the number as a square of another number and thus the square root of this number would be just $\left( a+b \right)$.

\begin{align} & {{a}^{2}}={{3}^{2}}=9 \\ & {{b}^{2}}={{0.5}^{2}}=0.25 \\ & 2ab=2\times 3\times 0.5=3 \\ \end{align}
${{a}^{2}}+{{b}^{2}}+2ab=9+0.25+3=12.25\text{ }.........\text{(1}\text{.1)}$
Which is the number given in the question. However, using the formula ${{a}^{2}}+{{b}^{2}}+2ab={{\left( a+b \right)}^{2}}$, we can rewrite equation (1.1) as
${{a}^{2}}+{{b}^{2}}+2ab={{\left( a+b \right)}^{2}}=12.25$
\begin{align} & {{\left( a+b \right)}^{2}}=12.25 \\ & \Rightarrow \sqrt{{{\left( a+b \right)}^{2}}}=\sqrt{12.25} \\ & \Rightarrow \sqrt{12.25}=a+b\text{ }...............\text{(1}\text{.2)} \\ \end{align}
As in this case a=3 and b=0.5, from equation (1.1), we write can write $\sqrt{12.25}$ as
$\sqrt{12.25}=a+b=3+0.5=3.5$