simplify the following radical expression by using the conjugate. \n\\frac{1}{\\sqrt{19}-\\sqrt{2}}…
simplify the following radical expression by using the conjugate. \n\\frac{1}{\\sqrt{19}-\\sqrt{2}} \n\\frac{\\sqrt{19}+\\sqrt{2}}{?}
Answer
Explanation:
Step1: Multiply numerator and denominator by conjugate
$$ \frac{1}{\sqrt{19}-\sqrt{2}}\times\frac{\sqrt{19}+\sqrt{2}}{\sqrt{19}+\sqrt{2}} $$
Step2: Expand denominator using difference of squares
$$ \frac{\sqrt{19}+\sqrt{2}}{(\sqrt{19})^2 - (\sqrt{2})^2} $$
Step3: Simplify denominator
$$ \frac{\sqrt{19}+\sqrt{2}}{19 - 2}=\frac{\sqrt{19}+\sqrt{2}}{17} $$
Answer:
$\frac{\sqrt{19}+\sqrt{2}}{17}$