Question

Find the square root of 7.29
a). 2.7
b). 2.3
c). 2.6
d). 2.4

Answer 1

Hint: In this question, we are given the number and we have to find its square root. Therefore, we can solve this question by the long division method to find the square root and obtain the answer to the given question.

Complete step-by-step answer:
As we have to find the square root of 7.29, we have to write it as \[\bar{0}\bar{7}.\bar{2}\bar{9}0000\] i.e. we should pair up the digits in pairs of 2 before and after the decimal place, as we take pairs of digits while calculating the square root.
In the long division method of finding the square root, we have to first find the square of a number which is closest to the first pair that is 07. We know that ${{2}^{2}}=4<7$ and ${{3}^{2}}=9>7$, therefore we should divide 7 by 2 first to obtain
$2\overset{2}{\overline{\left){\begin{align}
  & 07.2900 \\
 & -4 \\
 & 3.29 \\
\end{align}}\right.}}$
Thus, the digit before the decimal point in $\sqrt{7.29}$ should be 2……………………….(1.1)
We get the remainder as 3.29 and have taken down the next two digits after the decimal place. Now, we can put a decimal point in the quotient and write the remainder as 329. Then, we should double the divisor in the first step that is take the divisor as $2\times 2=4$ and try to find out a number of the form 4x such that $4x\times x$ is lower than but closest to 329.
As $47\times 7=329$ we should divide the remainder in the first step i.e. 329 by 47 to get
$47\overset{7}{\overline{\left){\begin{align}
  & \text{ 329} \\
 & -329 \\
 & \text{ 0} \\
\end{align}}\right.}}$

Thus, the digit at the first place after the decimal point in $\sqrt{7.29}$ should be 7……………………….(1.2)
Thus, from equations (1.1) and (1.2), we obtain
$\sqrt{7.29}=2.7$
This matches option (a) of the question. Therefore, option (a) is the correct answer.

Note: We could also have found the solution to this question by writing 7.29 as\[7.29=\text{ }4+2.8+0.49={{2}^{2}}+2\times 2\times 0.7+{{0.7}^{2}}\] . Now, we could have used the formula ${{a}^{2}}+{{b}^{2}}+2ab={{\left( a+b \right)}^{2}}$ with a=2 and b=0.7 to obtain $7.29={{\left( 2+0.7 \right)}^{2}}={{2.7}^{2}}$ and hence that the square root of 7.29 is 2.7 which is same as obtained in the solution.