4. Given are the numbers $a=-8$ and $b=36$.

a) Calculate the value of the expression $||a|-2 \sqrt{b}|-\frac{1}{2}|\sqrt[3]{a}|$.

b) Solve the equation $|x-\sqrt[3]{a}|=\sqrt{b}$.
4. a) In the given expression, we insert the appropriate numbers: $\left.||-8|-2 \sqrt{36}|-\frac{1}{2} \sqrt[3]{-8}|=| 8-12 \right\rvert\,-\frac{1}{2} \cdot 2=4-1=3$.

b) We simplify the equation $|x-\sqrt[3]{-8}|=\sqrt{36}$: $|x+2|=6$. From this, we conclude $x+2= \pm 6$ and obtain the solutions $x_{1}=4$ and $x_{2}=-8$.

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-07.jpg?height=91&width=1602&top_left_y=1251&top_left_x=244)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-07.jpg?height=60&width=1551&top_left_y=1329&top_left_x=298)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-07.jpg?height=49&width=1548&top_left_y=1386&top_left_x=297)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-07.jpg?height=51&width=1602&top_left_y=1502&top_left_x=244)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-07.jpg?height=51&width=1551&top_left_y=1551&top_left_x=298)