Question

provethat root 5
is irration​

Answer 1

Answer:

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Answer 2

$\huge\red{\mathfrak{Answer}}$

For proving √5 as a Rational Number, let us consider it as in the form of $\frac{a}{b}$

And , we know b is never equal to 0.

Therefore,

$\: \: \: \: \sqrt{5} = \frac{a}{b} \\ \\ \sqrt{5b} = a \\ \\ Squaring \: Both \: Sides \\ \\ {( \sqrt{5b)}^{2} } = {a}^{2} \\ \\ 5 {b}^{2} = {a}^{2} \\ \\ \frac{{a}^{2}}{5} = {b}^{2} \\ \\ now \\ \\ \frac{a}{5} = c \\ \\ 5 \times c = a \\ \\ = > 5c = a \\ \\ 5 {b}^{2} = {a}^{2} \\ \\ as \: we \: know \: a = 5c \\ \\ 5 {b}^{2} = 5 {c}^{2} \\ \\ 5 {b}^{2} = 25 {c}^{2} \\ \\ {b}^{2} = \frac{1}{5} \times 25 {c}^{2} \\ \\ {b}^{2} = 5 {c}^{2} \\ \\ \frac{ {b}^{2} }{5} = {c}^{2} \\ \\ 5 \: is \: divided \: by \: both \: a \: and \: b \\ \\ threfore \\ \\ \sqrt{5} \: is \: irraional$

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