The number 2+72−7\frac{$$\sqrt{2}$$ + $$\sqrt{7}$$}{\sqrt{2 - $$\sqrt{7}$$}}2−72+7is:

Given:2+72−7\\frac{$$\\sqrt{2}$$ + $$\\sqrt{7}$$}{\\sqrt{2 - $$\\sqrt{7}$$}}2−72+7Concept Used:An irrational number is a real number that cannot be expressed as a ratio of integers; for example, 2\\sqrt 22 is an irrational number. We cannot express any irrational number in the form of a ratio, such as pq\\frac pqqp, where p and q are integers, q≠0.Solution:2+72−7\\frac{$$\\sqrt{2}$$ + $$\\sqrt{7}$$}{\\sqrt{2 - $$\\sqrt{7}$$}}2−72+7=2+72−7×2−72−7\\frac{$$\\sqrt{2}$$ + $$\\sqrt{7}$$}{\\sqrt{2 - $$\\sqrt{7}$$}}\\times\\frac{\\sqrt{2 - $$\\sqrt{7}$$}}{\\sqrt{2 - $$\\sqrt{7}$$}}2−72+7×2−72−7=2+7×2−72−7×2+72+7\\frac{$$\\sqrt{2}$$ + $$\\sqrt{7}$$\\times \\sqrt{2 - $$\\sqrt{7}$$}}{2 - $$\\sqrt{7}$$} \\times \\frac{2 +$$\\sqrt{7}$$}{2 + $$\\sqrt{7}$$}2−72+7×2−7×2+72+7=(2+7)×2−7×(2+7)4−7\\frac{($$\\sqrt{2}$$ + $$\\sqrt{7}$$)\\times \\sqrt{2 - $$\\sqrt{7}$$}\\times (2 +$$\\sqrt{7}$$)}{4 - 7}4−7(2+7)×2−7×(2+7)=(2+7)×2−7×(2+7)−3\\frac{($$\\sqrt{2}$$ + $$\\sqrt{7}$$)\\times \\sqrt{2 - $$\\sqrt{7}$$}\\times (2 +$$\\sqrt{7}$$)}{-3}−3(2+7)×2−7×(2+7)We can say that , above expression is an irrational number.