Exercises: Square Roots

Solve the following equations.

$x^{2} = 16$

For this task you need the following basic knowledge: Square Roots
$\begin{array}{clll} x^{2} & = 16 & | \sqrt{} \\ \sqrt{x^{2}} & = \sqrt{16} \\ | x | & = 4 \end{array}$
The solutions are $x_{1} = 4$ , $x_{2} = - 4$ .
$x^{2} = 0$

For this task you need the following basic knowledge: Square Roots
$\begin{array}{clll} x^{2} & = 0 & | \sqrt{} \\ \sqrt{x^{2}} & = \sqrt{0} \\ | x | & = 0 \end{array}$
The solution is $x = 0$ .
$x^{2} + 2 = 11$

For this task you need the following basic knowledge: Square Roots
$\begin{array}{clll} x^{2} + 2 & = 11 & | - 2 \\ x^{2} & = 9 & | \sqrt{} \\ \sqrt{x^{2}} & = \sqrt{9} \\ | x | & = 3 \end{array}$
The solutions are $x_{1} = 3$ , $x_{2} = - 3$ .
$4 + x^{2} = 2$

For this task you need the following basic knowledge: Square Roots
$\begin{array}{clll} 4 + x^{2} & = 2 & | - 4 \\ x^{2} & = - 2 & | \sqrt{} \\ \sqrt{x^{2}} & = \sqrt{- 2} \end{array}$
There is no solution here. You cannot take a root of a negative number.

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