Question

prove that 5+2√3 is an irrational number​

Answer 1

Answer:

Irrational number are those numbers which are non-terminating and non-recurring. 2√3 is an irrational number and if we add 5 in it then it is also an irrational number.

√3=1.73205...

2√3=1.2539.....

so, 5+1.2539....

= 6.2539..... which is also non-terminating and non-recurring so it is an irrational number

hope it helps you

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Answer 2

Answer:

Let us assume that (5−2

3

) is a rational.

Subtract given number from 5, considering 5 is a rational number.

as we know Difference of two rational number is rational.

⇒5−(5−2

3

) is rational

⇒2

3

is rational

Which is only possible is 2 is rational and

3

is rational

As we know product of two rational number is rational.

But the fact is

3

is an irrational

which is contradictory to our assumption

(5−2 ✓3 ) is an irrational number.