Question

prove √5-√3 is not a rational number

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Answer 1

Answer:

ok I am answering this is not a rational number what you do hair because if v is not a

Answer 2

Answer:

Step-by-step explanation:

• Let us assume that √5 - √3 is a rational number.

=> √5 - √3 =  

Here .. a and b are co-prime numbers.

Now, squaring on both sides.

=> (√5 - √3)² =  

(a + b)² = a² + b² + 2ab

=> (√5)² + (√3)² - 2(√5)(√3) =  

=> 5 + 3 - 2√15 =  

=> 8 - 2√15 =  

=> - 2√15 =  

=> √15 =  

Here ...

is a rational number.

So, √15 is also a rational number. But we know that √15 is irrational number.

So, our assumption is wrong.

√5 - √3 is a irrational number

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