Question

Find the square root of 104 correct to 2 decimal places

Answer 1

Hint: A square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x For example, 4 and −4 are square roots of 16, because \[{4^2} = {( - 4)^2} = 16\]

Complete step-by-step answer:
We can do this by finding some factors of the number 104. So the lowest by which we can divide 104 is 2.
So the number becomes 52 and then again if we divide it by 2 we will get 26. Now as 26 is an even number it will again be divisible by 2. So we will left with 13
Which means that \[104 = 2 \times 2 \times 2 \times 13\]
We know if we square root in both the sides, the numbers which are occurring twice will come out of the root once.
Which means that \[\sqrt {104} = \sqrt {2 \times 2 \times 2 \times 13} \]
Hence we are left with
\[\begin{array}{l}
\therefore \sqrt {104} = 2\sqrt {2 \times 13} \\
 \Rightarrow \sqrt {104} = 2\sqrt {26}
\end{array}\]
Now we know the value of \[\sqrt {26} = 5.09\]
So by putting the value of \[\sqrt {26} \]
We will get
\[\begin{array}{l}
 \Rightarrow \sqrt {104} = 2\sqrt {26} = 2 \times 5.09\\
 \Rightarrow \sqrt {104} = 10.18
\end{array}\]
So the final answer is 10.18

Note: We cannot have square roots of negative numbers as we know that square of any integer is positive. But the square root can have both + and minus signs. But if we try to find the value of any -ve integer it will go to the complex number domain.