Math, asked by jeevan7050005, 9 months ago

Prove that (3-
 \sqrt{5}
3) is irrational.​

Answers

Answered by Anonymous
1

QUESTION:

\red {prove \: that \: 3 -  \sqrt{5} is \: irrational}

ANSWER:

Let,

3-root 5 is a rational number in the form of a by b where a and b are Co prime.

\blue {According \: to \: statement}

3 -  \sqrt{5}  =   \frac{a}{b}

 -  \sqrt{5}  =  \frac{a}{b}  - 3 \\

\orange {(taking \: lcm \: in \: rhs \: side)}

 -  \sqrt{5}  =  \frac{a - 3b}{b}

 \sqrt{5}  =  \frac{ - (a - 3b)}{b}

Hence, here contradiction arises as we know that root 5 is a irrational number but we let 3-root 5 as a rational number.

Hence proved.

Additional information :

☆Rational numbers :

Numbers that can be expressed in the form of p by q where p and q are integers and q is not equal to zero.

eg. 4/3; 2/4 etc.

☆Irrational numbers :

Real numbers which non terminating and non repeating

eg, value of pie.

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