Show that 3-2 is an irrational number-

Assume 3+√2 is rational,then 3+√2=p/q = gt;= gt; √2=p/q−3 Let 3 be equal to x/y = gt;= gt; √2=p/q−x/y √2=py−qx/qy Which contradicts the fact that √2 is ...

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Standard X

Mathematics

Proof by Contradiction

Show that 3+√...

Question

Show that $3 + \sqrt{2}$ is an irrational number.

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Solution

Assume 3+√2 is rational,then 3+√2=p/q

=>=> √2=p/q−3

Let 3 be equal to x/y

=>=> √2=p/q−x/y

√2=py−qx/qy

Which contradicts the fact that √2 is irrational

Hence,3+√2 is irrational.

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Show that 3+√2 is an irrational number.

Assume 3+√2 is rational,then 3+√2=p/q =>=> √2=p/q−3 Let 3 be equal to x/y =>=> √2=p/q−x/y √2=py−qx/qy Which contradicts the fact that √2 is irrational Hence,3+√2 is irrational.

Show that $3 + \sqrt{2}$ is an irrational number.

Assume 3+√2 is rational,then 3+√2=p/q

=>=> √2=p/q−3

Let 3 be equal to x/y

=>=> √2=p/q−x/y

√2=py−qx/qy

Which contradicts the fact that √2 is irrational

Hence,3+√2 is irrational.