Question

What is $x$ in ${{x}^{2}}=17$?

Answer 1

Hint: To obtain the value of $x$ from the given equation use square root method. Firstly we will write the expression given in the question which is ${{x}^{2}}=17$ then we will take square root on both sides of the equation. Finally we will simplify the equation further and get the two values of $x$ as it is a quadratic equation.

Complete step by step answer:
The equation is given as below:
${{x}^{2}}=17$
Now we will take square root on both sides as below:
$\sqrt{{{\left( x \right)}^{2}}}=\pm \sqrt{17}$
Next we will simplify the above equation as below:
$\begin{align}
  & \Rightarrow {{\left( {{x}^{2}} \right)}^{\dfrac{1}{2}}}=\pm \sqrt{17} \\
 & \Rightarrow x=\pm \sqrt{17} \\
\end{align}$
Now using a calculator we will find the approximate value of square root of 17 which is:
$x\approx \pm 4.123$

Hence, the $x$ in equation ${{x}^{2}}=17$ is $\pm 4.123$

Note: Quadratic equations are those which have an unknown variable with highest power as 2. If the equation contains the variable with power 2 only we can straightly take the square root of the equation to obtain the answer. But if the equation has an unknown variable with power 1 also then we use a quadratic formula to solve the equation. The value obtained of the unknown variable is also known as the root of the equation which satisfies the equation completely. If the equation is quadratic it always has two roots that is the reason we take plus and minus both values. The roots can be real or complex in nature depending on the equation. When we get a not perfect square value under the square root sign we take help of the calculator or try to get the approx value using another method.