Exercises: Square Roots - learn with Serlo!

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Solve the following equations.

$\quad x^2=16$

For this task you need the following basic knowledge: Square Roots
$\def\arraystretch{1.25} \begin{array}{clll}\ x^2&=16 \quad &|\sqrt{\quad}\\\ \sqrt{x^2}&=\sqrt{16}\\\ |x|&=4\end{array}$
The solutions are $x_{1} = 4$ , $x_{2} = - 4$ .
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$\quad x^2=0$

For this task you need the following basic knowledge: Square Roots
$\def\arraystretch{1.25} \begin{array}{clll}\ x^2&=0 \quad &|\sqrt{\quad}\\\ \sqrt{x^2}&=\sqrt{0}\\\ |x|&=0\end{array}$
The solution is $x = 0$ .
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$\quad x^2+2=11$

For this task you need the following basic knowledge: Square Roots
$\def\arraystretch{1.25} \begin{array}{clll}\ x^2+2&=11 \quad &|-2\\\ x^2&=9\quad&|\sqrt{\quad}\\\ \sqrt{x^2}&=\sqrt{9}\\\ |x|&=3\end{array}$
The solutions are $x_{1} = 3$ , $x_{2} = - 3$ .
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$\quad 4+x^2=2$

For this task you need the following basic knowledge: Square Roots
$\def\arraystretch{1.25} \begin{array}{clll}\ 4+x^2&=2 \quad &|-4\\\ x^2&=-2\quad&|\sqrt{\quad}\\\ \sqrt{x^2}&=\sqrt{-2}\end{array}$
There is no solution here. You cannot take a root of a negative number.
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