Question

prove that 5-root 3 is irrational. given that root 3 is irrational.
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Answer 1

Answer:

Brainly.in

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Secondary School Math 5 points

Prove that 5 - root 3 is irrational

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Answers

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batradivjyot25

batradivjyot25 Ace

Hey dear here is your answer ^_^

⭐Let us assume that 5 - root 3 is rational. Then it can be written in the form

5 - root3 = p/q

or 5 - p/q = root3

It implies root3 is a rational number [Since 5 - p/q are rationals]

But this contradicts to the fact that root 3 is irrational. Hence our supposition was wrong. Therefore 5 - root 3 is irrational.

CHEERZ!

Hope it helped you out ⭐^_^⭐

Thanks ⭐(^^)⭐

Answer 2

Given :-

• √3 is an irrational number

To Prove :-

• 5 - √3 is an irrational number

Solution :-

Consider 5 - √3 be a rational number

We can write this rational number as p/q form where q not equal to zero

5 - √3 = p/q

5 - p/q = √3

(5q - p)/q = √3

Since , both p and q are integers

Now ,

(5p - q)/q is a rational number and  √3 is also a rational number

But our assumption is wrong because √3 is an irrational number

Thus , 5 - √3 is an irrational number

Hence , proved