Question

Find square root of \[3\] correct to \[2\] places of decimals.

Answer 1

Hint: The square root of a number is a number whose square is equal to the original number. In other words, a number raised to the power of 0.5 is known as the square root of the number. To find the square root of the number we can use the prime factorisation method and the long division method. But here, as the number is single digit so, we have to use the long division method to determine the square root.



Complete step by step solution:
To find the square root of a number by long division method, we need to follow the following steps:
Step-I: First make an estimate by selecting that number whose roots are perfect squares. So your number lies between those roots.
Step-II: Divide that number by one of those square roots.
Step-III: We have to continue the process till we cannot achieve the average result of step \[2\]and the root.
Step-IV: Use this result we get in S-III until accuracy is not achieved.

	$1.7320508$
$1$	$3.0000000$
$27$	$ 200 \\ 189 \\ $-
$343$	$ 1100 \\ 1029 \\ $-
$3462$	$ 7100 \\ 6924 \\ $-
$346405$	\[ 1760000 \\ 1732025 \\ \]-
$34641008$	$ 279750000 \\ 277128064 \\ $-
	$2621936$

Hence, the square root of\[3\]correct to\[2\] places of decimals is 1.73.


Note: Firstly, it is necessary to check whether the given number is a perfect square or not because we can easily find the square root value of a perfect square. For finding the square root of non-perfect squares, we use a long division method. Value of $\sqrt 3 $ is widely used in mathematics. Since root 3 is an irrational number, which cannot be represented in the form of a fraction. It means that it has an infinite number of decimals.