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.