Question

What is x in $x^2=28$ when x is a real number ?

Answer 1

Hint: Real numbers consist of both, rational and irrational numbers, as well as negative and positive integers. Consider all possible solutions to the given problem.

Complete step-by-step solution:
 In the given question, the value of \[{x^2=28}\] is to be determined by finding out the square root of \[{x^2}\]. The value of \[{x^2}\] is given as equal to 28. To find out the value of
\[x^2=28\] we have to find the square root of 28 since it is given that \[{x^2}\] equals 28. Hence we write the equation,
\[{x^2} = 28\]
On taking square root for both the sides, we have,
\[\sqrt {{x^2}} = \sqrt {28} \]
On simplifying these terms we have,
\[ \sqrt {{x^2}} = \sqrt {4 \times 7} \]
\[\Rightarrow \sqrt {{x^2}} = \sqrt {{{(2)}^2} \times 7} \]
\[\Rightarrow \sqrt {{x^2}} = \pm 2\sqrt 7 \]
Hence, the value of \[x\] equals \[ \pm (5.2915)\]. It is important to note here that in this solution, there are 2 possible values of\[x\], and both the values are accepted as possible answers, since in the question it is specified to us that \[x\] is a real number. Real numbers consist of both rational and irrational numbers, as well as negative and positive integers. In this case, the value of \[x\] comes out to be an irrational number since it is a non-terminating and non-repeating number, and because it is the square root of a number, both negative and positive values are accepted as solutions for the value of \[x\].

Note: It is important to consider all possible solutions to a given question. In this case, since we had to solve a quadratic equation, the answer came out to be the square root of a number, which gave a negative and a positive value, and since in this case real numbers were to be considered, both the values were accepted as possible values of \[x\]. This has to be kept in mind while solving quadratic or cubic equations.