Question

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Q.27 Prove that 3+v5 is an irrational number.
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Answer 1

Solution:

An irrational number is a number which cannot be expressed in the form of a/b where A and B are integers and B is non zero.

Let us assume that 3+ root5 is a rational number.

Now,

3+ root5 = a/b

root 5 =[( a/b )−3]

root5 =[( a-3b)/b]

Here, [(a−3b )/b]is a rational number.

But we know that root 5 is an irrational number.

So, [( a-3b)/b]is also a irrational number.

So, our assumption is wrong.

3+ root 5 is an irrational number