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Prove that 3+5√2 is irrational.

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Prove that 3+5√2 is irrational.

Posted by Account Deleted 7 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Nishi K 7 years, 6 months ago

Let us assume that 3+5√2is rational no. written in the form of p/q where p,q are integer. Suppose p,q have no any common factor . 3+2√5=p/q 5√2=p/q-3 √2 =1/5(p/q-3) Since, 1/5(p/q-3)is rational So, √2 is also a rational . This is contradicts the fact that √2 is irrational. Hence, 3+2√5 is irrational.

2Thank You

Shubham Kumar 7 years, 6 months ago

Let 3+5√2 is a rational number Then,3+5√2=p/q( rational number always in the form of p/q where q not equal to '0') 3+5√2=p/q 5√2=p/q-3 √2=p/q-3/5 But we know that √2 is an irrational no° . So , 3+5√2 is an irrational number.

2Thank You

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