Question

$prove \sqrt{p} \: + \sqrt q \: is \: a \: irrationl \: number$
class 10 chapter 1

Answer 1

Hey !!!

Let us assume that

√p + √q is rational no .and √p + √q = a

REARRANGING the term

√p = a -√q

squaring on both side we get .

(√p )² = (a -√q)²

p = a² + q - 2a√q

p - q² -q /2a = -√q

=> q² -p + q/2a = √q

=> q² - p + q/2a = √q

here q² - p + q / 2a is rational and it is equal to √q so √q is also rational no .

But , it is not possible

Here is contradiction is form that √q is rational . it is irrational

so, It is not possible that q² -p +q/2a is rational .

it is possible only that

√q is irrational so q² -p + q /2a is also irrational .

so, we can say that

√p + √q is rational no .

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Hope it helps you !!!

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