Question

given root 3 and root 5 are irrational no. prove that 2 root 3 +root 5 is an irrational no.​

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

Answer 2

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