Question

5√-32 simplify
help!​

Answer 1

-2

Explanation:

`\sqrt[n]{a}=b\iff b^n=a\\\\\sqrt[n]{a^n}=a\\\\\sqrt[5]{-a}=-\sqrt[5]{a}\\\\========================\\\\\sqrt[5]{-32}=\sqrt[5]{-2^5}=-\sqrt[5]{2^5}=-2`

`\text{If is}\ 5√(-32),\ \text{then:}\\\\5√(-32)=5√((16)(2)(-1))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=5\cdot√(16)\cdot\sqrt2\cdot√(-1)\qquad\text{use}\ i=√(-1)\\\\=5\cdot4\cdot\sqrt2\cdot i=20\sqrt2\ i`