Question

What if the simplest form of the radical expression?

Answer 1

`\large\boxed{(\sqrt2+\sqrt5)/(\sqrt2-\sqrt5)=-(7+2√(10))/(3)}`

Explanation:

`\text{Use}\ (a-b)(a+b)=a^2-b^2\ \text{and}\ (a+b)^2=a^2+2ab+b^2\\\\\\(\sqrt2+\sqrt5)/(\sqrt2-\sqrt5)=(\sqrt2+\sqrt5)/(\sqrt2-\sqrt5)\cdot(\sqrt2+\sqrt5)/(\sqrt2+\sqrt5)=((\sqrt2+\sqrt5)^2)/((\sqrt2)^2-(\sqrt5)^2)\\\\=((\sqrt2)^2+2(\sqrt2)(\sqrt5)+(\sqrt5)^2)/(2-5)=(2+2√((2)(5))+5)/(-3)\\\\=-(7+2√(10))/(3)`