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Show that that root 3 + root 5 the whole square is an irrational number |
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Answer» Answer: Let us ASSUME to the CONTRARY that (√3+√5)² is a rational number,then there exists a and b co-prime integers such that, (√3+√5)²=a/b 3+5+2√15=a/b 8+2√15=a/b 2√15=(a/b)-8 2√15=(a-8b)/b √15=(a-8b)/2b (a-8b)/2b is a rational number. Then √15 is ALSO a rational number But as we KNOW √15 is an irrational number. This is a CONTRADICTION. This contradiction has arisen as our assumption is wrong. Hence (√3+√5)² is an irrational number. please mark me as the brainliest.... |
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