Question

How do you find square root of $1256?$

Answer 1

Hint: Square root of a number “n” is another number “q” which will be equal to “n” when multiplied by itself. To simplify the given root check if it is a perfect square or not. If not, then surely its square root will be irrational, so better simplify it to smaller radical, rather than simplifying it to decimal places because irrational numbers have infinite number of decimals so better not to deal with it. Root of a perfect square is given as ${a^2} = \sqrt {a \times a} $.

Complete step by step solution:
We will first define and then simplify $\sqrt {1256} $. We begin with the definition and then answer some common questions about the square root of $1256$. Then, we will simplify $\sqrt {1256} $. In mathematical form, the square root of $1256$ is written as $\sqrt {1256} $ with the radical sign. The $\sqrt {1256} $ is a quantity $(n)$ that will equal $1256$ when multiplied by itself.
$n \times n = {n^2} = 1256$
Is $1256$ a perfect square?
When the square root of $1256$ is equal to the whole number, then $1256$ is a perfect square. The square root of $1256$ is not a whole number, as we have calculated below. So it is not a perfect square.
We will simplify it to smaller radical,
We can write $\sqrt {1256} $ as
$\sqrt {1256} = \sqrt {2 \times 2 \times 2 \times 157} \\
\therefore\sqrt {1256} = 4\sqrt {314} $

Therefore the simplified form of $\sqrt {1256} \;{\text{is}}\;4\sqrt {314}$.

Note: We know that negative times negative are equal to positive. Thus, not only does the square root of $1256$ have the positive answer we explained above, but also have the negative counterpart and is written with negative sign $\left( { - 4\sqrt {314} } \right)$
If you want the result in decimals then with the use of a calculator find the approximate value of $4\sqrt {314} $ or rather you can go with a long division method.