Question

Simplify the following irrational numbers
√12-√98+√18-√27
√125+√8-√32+√180
√72+√288+√50

Answer 1

Solution :-

1. $\sqrt{12}-\sqrt{98}+\sqrt{18}-\sqrt{17}$

=> $\sqrt{2 *2*3}-\sqrt{7*7*2}+\sqrt{3 * 3*2}-\sqrt{17}$

=> $2\sqrt{3}-7\sqrt{2}+3\sqrt{2}-\sqrt{17}$

=>$2\sqrt{3}-4\sqrt{2}-\sqrt{17}$

2. $\sqrt{125}+\sqrt{8}-\sqrt{32}+\sqrt{180}$

=> $\sqrt{5*5*5}+\sqrt{2*2*2}-\sqrt{2*2*2*2*2}+\sqrt{3*3*2*2*5}$

=> $5\sqrt{5}+2\sqrt{2}-4\sqrt{2}+6\sqrt{5}$

=>$11\sqrt{5}-2\sqrt{2}$

3. $\sqrt{72}+\sqrt{288}+\sqrt{50}$

=> $\sqrt{2*2*2*3*3}+\sqrt{2*2*2*2*2*3*3}+\sqrt{5*5*2}$

=> $6\sqrt{2}+12\sqrt{2}+5\sqrt{2}$

=> $23\sqrt{2}$

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