Question

Highschool surds maths

Answer 1

`\cfrac{8-√(18)}{√(2)}~~ = ~~a+b√(2) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{8-√(18)}{√(2)}\implies \cfrac{8-√(18)}{√(2)}\cdot 1\implies \cfrac{8-√(18)}{√(2)}\cdot \cfrac{√(2)}{√(2)}\implies \cfrac{(8-√(18))(√(2))}{(√(2))(√(2))}`

`\cfrac{8√(2)-√(18)\cdot √(2)}{√(2^2)}\implies \cfrac{8√(2)-√(18\cdot 2)}{2}\implies \cfrac{8√(2)-√(36)}{2} \\\\\\ \cfrac{8√(2)-6}{2}\implies \cfrac{8√(2)}{2}-\cfrac{6}{2}\implies 4√(2)-3\implies -3+4√(2) \qquad \begin{cases} a=-3\\ b=4 \end{cases}`