Prove that 3-2 -5 is irrational number-

Let 3 + 2√(5) is rational therefore 3 + 2√(5)=a/b (where a and b are any integer ) √(5)=a 3/2b because a 3/2b is rational therefore √(5) will also be rational b ...

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Byju's Answer

Standard IX

Mathematics

Addition and Subtraction of Rational Numbers

Prove that 3+...

Question

Prove that $3 + 2 \sqrt{5}$ is irrational number.

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Solution

Let $3 + 2 \sqrt{5}$ is rational
therefore $3 + 2 \sqrt{5} = \frac{a}{b}$ (where a and b are any integer )
$\sqrt{5} = \frac{a - 3}{2 b}$
because $\frac{a - 3}{2 b}$ is rational
therefore $\sqrt{5}$ will also be rational
but we know that,
$\sqrt{5}$ is irrational
that is our supposition is wrong
that is $3 + 2 \sqrt{5}$ is irrational.

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Prove that 3+2√5 is irrational number.

Let 3+2√5 is rational therefore 3+2√5=ab (where a and b are any integer ) √5=a−32b because a−32b is rational therefore √5 will also be rational but we know that, √5 is irrational that is our supposition is wrong that is 3+2√5 is irrational.

Prove that $3 + 2 \sqrt{5}$ is irrational number.