Question

Prove that√3- √7 is irrational​

Answer 1

hello buddy!!!!!✌

Answer:

let it be rational

means it is of form x/y where x and y are co prime integers and y not equal to 0

\sqrt{3} + \sqrt{7} = \frac{x}{y}

Squaring both sides....

3 + 7 + 2 \sqrt{21} = \frac{ {x}^{2} }{ {y}^{2} }

10 + 2 \sqrt{21} = \frac{ {x}^{2} }{ {y}^{2} }

\frac{ {x }^{2} - 10 {y}^{2} }{2 {y}^{2} } = \sqrt{21}

but it contradict the fact that x and y are co prime integers as root21 is irrational and x^2-10y^2/2y^2 is rational

this means our supposition is wrong

thus root3+root7 is irrational.

hope it helps you......✨✨♥✨✨

Answer 2

Answer:let it be rational

means it is of form x/y where x and y are co prime integers and y not equal to 0

Squaring both sides....

but it contradict the fact that x and y are co prime integers as root21 is irrational and x^2-10y^2/2y^2 is rational

this means our supposition is wrong

thus root3+root7 is irrational

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