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Prove that √3 + √5 is an irrational number, given that √3 is irrational |
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Answer» Answer: assume that √3+√5 be rational so we can say that √3+√5 will be p/q now, √3= p/q-√5 √3=p-√5q/q squaring both the sides 3= p²-2√5pq+5q/q² 3q²=p-2√5pq+5q 3q²-p-5q/pq=√5 the LHS is a rational number as it is of the form p/q how EVER we are seeing that the RHS is an IRRATIONAL number. SO ACCORDINGLY A RATIONAL NUMBER CAN NEVER BE EQUAL TO AN IRRATIONAL NUMBER. Step-by-step explanation: |
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