Question

Find the square root of 7744 by prime factorisation method.

Answer 1

Hint: In this problem, we first have to express the number 7744 in the form of prime factors. Then we have to arrange the number into groups of even power. By doing so we can easily evaluate the square root of 7744.

Complete step-by-step answer:
In mathematics, the number system is the branch that deals with various types of numbers possible to form and easy to operate with different operators such as addition, multiplication and so on. A common way of representing a large number is in the form of prime factors. Multiplying two whole numbers gives some product. The numbers that we multiply are factors of the product. Hence, a factor can be defined as a number which completely divides a number without leaving any remainder. For example, factors of 12 are 1, 2, 3, 4, 6 and 12.
Using the prime factorization method, we can express 7744 as:
$\begin{align}
  & 7744=2\times 2\times 2\times 2\times 2\times 2\times 11\times 11 \\
 & 7744={{2}^{6}}\times {{11}^{2}}\ldots (1) \\
\end{align}$
Now, taking the square root of equation (1), we get
$\begin{align}
  & \sqrt{7744}=\sqrt{{{2}^{6}}\times {{11}^{2}}} \\
 & \sqrt{7744}={{2}^{\dfrac{6}{2}}}\times {{11}^{\dfrac{2}{2}}} \\
 & \sqrt{7744}={{2}^{3}}\times 11 \\
 & \sqrt{7744}=8\times 11 \\
 & \sqrt{7744}=88 \\
\end{align}$
Hence the square root of 7744 is 88 by using the prime factorization method.

Note: The key step in solving this problem is the knowledge of the number system and different ways of representation of numbers. Apart from this, the concept of square root of a number must be clear. Also, the concept of prime factorisation is also required to solve this problem.