Math, asked by prachirathod2007, 5 months ago

Given that √2 is irrational, prove that (5+3√2 ) is an irrational number.

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Answers

Answered by suhaniiiiiiii

Please refer to the picture for solution.
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prachirathod2007: thanks for helping

Answered by Anonymous

Given that:-

√2 is irrational.

We know that the theorem The product of any irrational number with a rational number is irrational.

So, since we know 3 is a rational number,

3√2is irrational.

(3= 3/1 ;1¥0. )

Now we know that 3√2 is irrational.

Theorem: The sum of a rational number with an irrational number is irrational.

So, since we know 5 is a rational number, 5+3√2 is irrational.

Thus we proved that 5+3√2

is an irrational number.

prachirathod2007: thanks for helping

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Given that √2 is irrational, prove that (5+3√2 ) is an irrational number.​