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√2+√5 is irrational prove this |
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Answer» Answer: Given: √2+√5 We need to prove√2+√5 is an irrational number. Proof Let us ASSUME that √2+√5 is a RATIONAL number. A rational number can be written in the form of p/q where p,q are INTEGERS and q≠0 √2+√5 = p/q On squaring both SIDES we get, (√2+√5)² = (p/q)² √2²+√5²+2(√5)(√2) = p²/q² 2+5+2√10 = p²/q² 7+2√10 = p²/q² 2√10 = p²/q² – 7 √10 = (p²-7q²)/2q p,q are integers then (p²-7q²)/2q is a rational number. Then √10 is also a rational number. But this contradicts the FACT that √10 is an irrational number. Our assumption is incorrect √2+√5 is an irrational number. Hence proved. |
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