Question

prove that 3+5√2 as irrational is irrational?​

Answer 1

Answer:

Step-by-step explanation:

Let 3+5/2–√ be rational.

3+5/2–√=p/q

squaring both sides we get. (3+5/2–√)2=(p/q)2

59+30/2–√=(p/q)2

WE CAN WRITE:

2–√=(p2−59q2)/30q2

Lhs. Irrational Rhs. Rational

Not possible. So. 3+5/2–√ is irrational.

Answer 2

Answer:

(1) 3+5√2

➡️ let us assume that 3+5√2 is a rational number

rational number is of the form of p/q , a , b, E, Z and b ≠ 0 .

$3 + 5 \sqrt{2} = \frac{a}{b}$

$= 5 \sqrt{2} = \frac{a}{b} - 3$

$= 5 \sqrt{2} = \frac{a}{b} - \frac{3}{1}$

$= 5 \sqrt{2} = \frac{a}{b} - \frac{3}{1} \times \frac{b}{b}$

$= 5 \sqrt{2} = \frac{a}{b} - \frac{3b}{b}$

$= 5 \sqrt{2} = \frac{a - 3b}{b}$

$= \sqrt{2 } = \frac{a - 3b}{b} \times \frac{1}{5}$

$= \sqrt{2} = \frac{a - 3b}{5b}$

$\frac{a - 3b}{5b} \: is \: of \: the \: form \: of \: \frac{a}{b} \\ hence \: it \: is \: a \: rational \: number \: \\ but \: \sqrt{2} \: is \: a \: irrational \: number \\ the \: assume \: is \: false \: \\ 3 + 5 \sqrt{2} \: is \: an \: irrational \: number$

HENCE PROVED

HOPE THIS HELPS U

#Ravalika Rajula

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