Question

prove 3+2√5 is an irrational ​

Answer 1

Answer:

Answer:-

• Please refer to the attachment ✔️ ✔️

Answer 2

Step-by-step explanation:

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$\huge\bold\star\red{\underline{Answer:-}}$

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$\Large\bold\star\green{\underline{To\ prove:-}}$

$3+2\sqrt{5}$

$\large\bold\star\purple{\underline{Solution:-}}$

$\Longrightarrow$ Let us assume the opposite,

i,e., $3+2\sqrt{5}$

Hence, $3+2\sqrt{5}$ can be written in the form $\frac{a}{b}$

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

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

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

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

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

Here, $\sqrt{5}$ is irrational.

And, $\frac{a-3b}{2b}$ is rational.

Since, rational is unequal to irrational .

$\therefore$ , $3+2\sqrt{5}$ is irrational.

Hence proved.

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$\bold\star\red{\underline{That's\ all}}\star$

$\bold\star\orange{\underline{Hope\ it\ helps\ you}}\star$