Question

How do you find the square root of 203?

Answer 1

Hint: Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\]. Here we know that 203 is not a perfect square. We can find the square root of 203 using factors of 203.

Complete step-by-step solution:
Given, square root of 203.
That is, \[\sqrt {203} \]
203 can be factorized as,
\[203 = 1 \times 7 \times 29\]
We can see that there is no number which is multiplied twice,
\[
  \sqrt {203} = \sqrt {7 \times 29} \\
   = \sqrt 7 \times \sqrt {29} \\
\].
We need to know the value of \[\sqrt 7 \] and \[\sqrt {29} \].
We know \[\sqrt 7 = 2.646\] and \[\sqrt {29} = 5.385\]. Multiplying we have,
\[
  \sqrt {203} = 2.646 \times 5.385 \\
  \sqrt {203} = 14.249 \\
\].
(203 is already in the simplified form and we cannot find the factors which are multiplied twice.)

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number. To find the factors find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors. Follow the same procedure for these kinds of problems.