Question

The answer is 2(sign)21 I need help with the work

Answer 1

Using Pythagoras:

$4^2+x^2=10^2\Longrightarrow x^2=10^2-4^2=100-16\text{ = }84\Longrightarrow x\text{ = }\sqrt[]{84}$$x=\sqrt[]{84\text{ }}=\sqrt[]{2\cdot42}\text{ = }\sqrt[]{2\cdot2\cdot21}\text{ = }\sqrt[]{21\cdot2^2}\text{ =2}\cdot\sqrt[]{21}$

Answer:

$2\cdot\text{ }\sqrt[]{21}$