Question

Q.8) Prove that v5 is an irrational
number and hence show that 2-V5 is
also an irrational number. ( 5 marks)​

Answer 1

Answer:

Root 5=2.2360.... it can't be written in P/q form

Hence proved that it is an irrational number

2-root5

2-2.2360

O.236

it can't be written in p/q form so it is also a irrational number

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Answer 2

Step-by-step explanation:

Solution

Let

$\sqrt{5} \ is \: a \: rationa \: number$

$\sqrt{5} = \frac{p}{q} (q \: does \: not \: = 0)$

Where p and q are integers.

$\sqrt{5q} = p$

Squaring both side we get

$5 {q}^{2} = {p}^{2}$

${p}^{2} is \: divisible \: by \: 5$

$</p><p>p \: is \: al \: so \: divisible \: by \: 5$

Put in equation above

P = 5b

$5 {q}^{2} = {p}^{2}$

$5 {q}^{2} = {(5b)}^{2}$

$5 {q}^{2} = 25 {b}^{2}$

${q}^{2} = 5 {b}^{2}$

${q}^{2} \: is \: divisible \: by \: 5$

$q \: is \: also \: divisible \: by \: 5$

So,

Our Contradiction has arisen because of our assumption that root 3 is rational number

Then,

We conclude that root 3 is irrational number

• HENCE PROVE

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