Question

Find out the square root of $$73$$.

Answer 1

Hint: According to the question, square root of $$73$$ means $$\sqrt{73}$$. $$\sqrt{73}$$ is an irrational number. So, it cannot be simplified any further. So, to find out its square root, we have to solve it by using the long division method.

Complete step-by-step answer:
We will find out the square root of $$73$$ by taking the help of a long division method.
First, we will pair the digits from one’s place and put the horizontal bar to indicate pairing.
Now, we will find a number which on multiplication with itself gives the number either equal to less than $$73$$:
$$\Rightarrow 8\times 8=64$$
$$64$$ is less than $$73$$. The difference is $$9$$ and quotient is $$8$$.
Now we will bring two $$0$$ down to multiply the quotient with $$2$$. We will get $$16$$ as a result, which will be the starting digit of the new divisor and $$5$$ will be placed at its one’s place because $$165\times 5=825$$. Now, the remaining part is $$75$$ and brings two $$0$$ down.
Now, the quotient is $$85$$, and $$85\times 2=170$$, which will be the new divisor. Now, put $$4$$ on its one’s place because $$170\times 4=6816$$.
Now, the new divisor will be $$684$$, and we will bring the two $$0$$ down. Quotient will be $$854$$. $$854\times 2=1708$$, which will be the starting digit of the new divisor. $$4$$ will be placed at one’s place because $$1708\times 4=68336$$.
Now, the divisor is $$64$$.
Therefore, the square root of $$73$$ is $$8.544$$ and on repeating this further we get as $$8.54400374...$$

Note: The square of square root of $$73$$ will be $$73$$. A rational number should have a terminating decimal part or non-terminating decimal part with repeating pattern. You will not get any integers whose square will give you $$73$$. Hence, $$\sqrt{73}$$ is an irrational number.