Question

Given root 3 and root 5 are irrational numbers , prove that 2 root 3 +root 5 is an irrational number

Answer 1

Answer:

To Prove :  2√3 + √5 is irrational

we know that √3 & √5 are irrational numbers.

Now we use result which states that

Product of a rational and an irrational no. is an irrational no.

⇒ 2√3 is irrational no.

Now. according to closure property of irrational no.

Sum of two irrational no. is also an irrational no.

⇒ 2√3 + √5 is an irrational no.

Hence Proved

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