How do you solve ${x^2} - 8 = 0$?

Hint: First of all, by using the transposition method shift 8 in either side of the equation. Then, do the square root on both sides of the equation. We will get the two values for $x$, use them according to the situation given in other questions.

Complete Step by Step Solution:
We have been given the question, that we have to solve for \[x\] in the equation, ${x^2} - 8 = 0$. So, first of all, we will simplify the given equation so that we can simply find the value of \[x\] in the equation, ${x^2} - 8 = 0$. Therefore, we will use the transposition method for solving further this question. But we should know how this transposition method works.
In the transposition method, the number is shifted to another side of the equation by which the function of the mathematical operators is changed. In this method, when the plus sign is shifted to another side then it changes to the subtraction sign and when the subtraction sign is shifted, it changes to the addition sign. When multiplication is shifted to another side it changes to division and when division is shifted to another side it changes to a multiplication sign.
According to the question, the equation given is ${x^2} - 8 = 0$ so, we will use the transposition method to shift -8 to another side, we get –
$ \Rightarrow {x^2} = 8$
When we do the square root of any number, we get the two values of the square root of that number i.e., one of negative and another of positive
Now, doing the square root on both sides of the equation ${x^2} = 8$, we get –
$ \Rightarrow x = \pm 2\sqrt 2 $

Hence, the values of $x$ are $ + 2\sqrt 2 $ and $ - 2\sqrt 2 $.

Note:
The polynomial equation is the algebraic expression that contains alphabetical as well as numerical values but when the alphabets representing an unknown variable quantity are raised to some power such that the exponent is non – negative integer then, the algebraic expression becomes a polynomial equation.