Question

Simplify:
(a) $\sqrt[4]{481}-\sqrt[5]{532}$
(b) If $2$ is zero of the polynomial $P\left(x\right)=2x^2-3x+5k$, find $K$?

Answer 1

$\sqrt[4]{481}-8\sqrt[3]{3343}+15\sqrt[5]{532}+\sqrt{332}$

$=\sqrt[4]{43\times 3\times 3\times 3}-8\left(\sqrt[3]{37\times 7\times 7}\right)+15\left(\sqrt[5]{52\times 2\times 2\times 2\times 2}\right)+\sqrt{332}$

$=\sqrt[4]{43^4}-8\left(\sqrt[3]{33^7}\right)+15\sqrt[5]{52^5}+18.22$

$=3-8\times 7+15\times 2+18.22$

$=3-56+30+18.22=-4.78$