Question

Find the square root of the following:
$1043.29$

Answer 1

Hint: In this question we have been given with a number of which we have to find its square root. We can see that the given number is in the form of a decimal number therefore, we will first convert this number into the fraction by multiplying and dividing the number with a same term. After the number is converted into a fraction, we will take the square root of the numerator and the denominator. We will then divide then simplify the terms in the fraction to get the required solution.

Complete step by step answer:
We have the term given to us as:
$=1043.29$
We have to take the square root of the number therefore; we can write it as:
$=\sqrt{1043.29}$
Now we have the term in the form of a decimal. On multiplying and dividing the term by $100$, we get:
$=\sqrt{1043.29\times {\displaystyle \frac{100}{100}}}$
Now on multiplying the numerator with $100$, the decimal part gets removed, we can write it as:
$=\sqrt{{\displaystyle \frac{104329}{100}}}$
Now we can split the square root in the numerator and denominator and write the expression as:
$={\displaystyle \frac{\sqrt{104329}}{\sqrt{100}}}$
Now we know that $\sqrt{104329}=323$ and the square root of $\sqrt{100}=10$, therefore on substituting it in the expression, we get:
$={\displaystyle \frac{323}{10}}$
Now on simplifying the fraction, we get:
$=32.3$, which is the required answer.

Therefore, we have the square root of $1043.29$ as $32.3$, which is the required solution.

Note: It is to be remembered that when the same term is multiplied and divided by another term, the value of the term does not change. It is to be remembered that the square root of negative numbers does not exist in the real numbers range. For these types of situations imaginary numbers are used which give the square root of negative numbers using $i$ which has a value as $\sqrt{-1}$.