Prove that 2√3 + √5 is an irrational number. Also check whether

(2√3 + √5). (2√3 - √5) is rational or irrational.

We have to prove that is irrational.

We can prove the above result by the method of contradiction as-

Let be a rational number which can be expressed in the form of p/q where q is not equal to 0 and p and q are relatively prime.

Hence,

Since p and q are integers and hence is a rational number.

So this implies that is a rational number which contradicts the fact that is irrational.

Hence our assumption is wrong and is irrational.

Now,

Hence this is a rational number.

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DEAR JYOTHIWE CAN DO IT BY THIS WAY.ASSUME IT AS RATIONAL. SO ,WE CAN WRITE IT AS ab.

2ROOT3A=B SQUARE IT THEN 2ROT 3 WILLBECAME 12{4*3=12}, 12ASQUARE=B SQUARE. THEN 12 DIVIDES B SQUQRE AND B. THEN 12A SQUARE IS = C SQUARE. THEREFORE 12 DIVIDES C SQUARE AND C. THEREFORE 2ROOT3 IS RATIONALBUT IT CONTRA DICTS THAT IT IS IRRATIONAL.

 
 
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