Question

Prove that 2 - √3 is irrational,given that √3 is irrational.​

Answer 1

Step-by-step explanation:

Given

3

is irrational number

Let 2+

3

is rational number.

then 2+

3

=

q

p

3

=

q

p−2q

Since

3

is irrational number but

q

p−2q

is rational it mean

irrational = rational

which contradict,

∴ our assumption is wrong and

2+

3

is irrational number.

Answer 2

Answer:

we know that 2-root3 is a rational number to prove this we take an contrart that this number is a rational number.

Now,

2-root3=p/q

root3=p/q+2

hence,

we know that root3 is a irrational number therefore 2-root3 will be a irrational number

Step-by-step explanation:

this answer will satisf in 3 number if it will come in 5 number also prove that how root3 is a irrational

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