Question

Prove that 13√13 is irrational
Hint
13√=13×√3√3√=13.3-√13=13×33=13.3​

Answer 1

Answer:

Let us assume 13+25(2)

1/2

is a rational number

we know that 13 is rational number.

Now subtract 13 from 13+25(2)

1/2

and we know that the difference of two rational number is also a rational number

That mean, 13+25(2)

1/2

−13=25(2)

1/2

is a rational number

We know 25 is rational number and product of two rational number is also a rational number

=> [25(2)

1/2

]×

25

1

=(2)

1/2

is not a rational number

This means that

13+25(2)

1/2

is a irrational number.

Step-by-step explanation:

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