Question

Solve \[{x^2} = 7\]?

Answer 1

Hint: Here we will first take square root on both sides of the algebraic equation and then we will convert the square root into the power form. We will use some basic properties of the exponents and then we will simplify the equation further using some mathematical operations. After simplifying the equation, we will get the required solution to the given algebraic equation.

Complete step by step solution:
Here we need to solve the given algebraic equation and the given algebraic equation is \[{x^2} = 7\].
The given equation is the quadratic equation and the degree of the equation is 2.
Now, we will take the square root on both sides of the algebraic equation.
\[ \Rightarrow \sqrt {{x^2}} = \sqrt 7 \]
Now, we will convert the square root into the power form.
\[ \Rightarrow {x^{2 \times \dfrac{1}{2}}} = \pm \sqrt 7 \]
Now, we will multiply the numbers in the exponent of the variable in the left-hand side expression.
\[ \Rightarrow x = \pm \sqrt 7 \]

Therefore, the value of \[x\] is equal to \[ \pm \sqrt 7 \]. Hence, this is the required solution to the given algebraic equation.

Additional information:
We know that an algebraic equation is defined as the equalities that contain the variables and the constants which are combined using mathematical operations like addition, subtraction, multiplication, and division. The given algebraic equation is the quadratic equation as the highest power of the variable is 2 here i.e. the degree of the given algebraic equation is 2.

Note:
We can also solve this question using the quadratic formula.
We will first convert the given equation into a general quadratic equation \[a{x^2} + bx + c = 0\].
Thus, the equation becomes \[{x^2} - 7 = 0\].
Here, \[a = 1,b = 0\] and \[c = - 7\]
Now using the quadratic formula \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\], we get
\[x = \dfrac{{ - \left( 0 \right) \pm \sqrt {{0^2} - 4 \times - 7} }}{2}\]
Simplifying the expression, we get
\[ \Rightarrow x = \dfrac{{ \pm 2\sqrt 7 }}{2}\]
Dividing the terms, we get
\[ \Rightarrow x = \pm \sqrt 7 \]