Question

Сократите дробь:
а) $\frac{\sqrt{28} -\sqrt{8} }{\sqrt{7} -\sqrt{2} }$
б) $\frac{\sqrt{60} +\sqrt{20} }{\sqrt{45}+\sqrt{135} }$

Answer 1

Ответ:

$a)\ \ \dfrac{\sqrt{28}-\sqrt{8}}{\sqrt7-\sqrt2}=\dfrac{\sqrt{4\cdot 7}-\sqrt{4\cdot 2}}{\sqrt7-\sqrt2}=\dfrac{2\sqrt7-2\sqrt2}{\sqrt7-\sqrt2}=\dfrac{2\cdot (\sqrt7-\sqrt2)}{\sqrt7-\sqrt2}=2\\\\\\b)\ \ \dfrac{\sqrt{60}+\sqrt{20}}{\sqrt{45}+\sqrt{135}}=\dfrac{\sqrt{4\cdot 15}+\sqrt{4\cdot 5}}{\sqrt{9\cdot 5}+\sqrt{9\cdot 15}}=\dfrac{2\sqrt{15}+2\sqrt5}{3\sqrt5+3\sqrt{15}}=\dfrac{2\cdot (\sqrt{15}+\sqrt5)}{3\cdot (\sqrt5+\sqrt{15})}=\dfrac{2}{3}$