Question

How do you solve ${x^2} = 5?$

Answer 1

Hint: Here we will use the concept of the square and square-root and will find the values of “x” accordingly. Since the power of “x” is two, so we will get two values for it.

Complete step-by-step solution:
Take the given expression:
${x^2} = 5$
Take the square root on both sides of the equation.
$\sqrt {{x^2}} = \sqrt 5 $
Square and square root cancel each other on the left hand side of the equation. Also, always remember that the square of the positive term or the negative term always gives the positive term.
$ \Rightarrow x = \pm \sqrt 5 $
The above equation implies that the values can be –
$x = \sqrt 5 $or $x = - \sqrt 5 $

Additional Information: Constants are the terms with fixed value such as the numbers it can be positive or negative whereas the variables are terms which are denoted by small alphabets such as x, y, z, a, b, etc. Be careful while moving any term from one side to another. Cube is the product of same number three times such as ${n^3} = n \times n \times n$ for Example cube of $2$ is ${2^3} = 2 \times 2 \times 2$ simplified form of cubed number is ${2^3} = 2 \times 2 \times 2 = 8$. and cube-root is denoted by $\sqrt[3]{{{n^3}}} = \sqrt {n \times n \times n} = n$ For Example: $\sqrt[3]{8} = \sqrt[3]{{{2^3}}} = 2$ Do not be confused in square and square-root similarly cubes and cube-root, know the concepts properly and apply accordingly.

Note: Know the concepts of squares and cubes. Square is the number multiplied itself and cube it the number multiplied thrice. Square is the product of same number twice such as ${n^2} = n \times n$ for Example square of $2$ is ${2^2} = 2 \times 2$ simplified form of squared number is ${2^2} = 2 \times 2 = 4$ and square-root is denoted by $\sqrt {{n^2}} = \sqrt {n \times n} $ For Example: $\sqrt {{2^2}} = \sqrt 4 = 2$