Question

prove that 15+17 √3 is an irrational number

Answer 1

√3 is irrational. it multiply and sum with rational then resultant is irrational

Answer 2

Answer:

Step-by-step explanation:

15+17 √3

Let √3 be rational number, so it can be written as p/q where q is not equal to 0 and p and q is co prime number

√3 =  p/q

√3 * q = p

Squaring both side, we get

3 * q² = p²

3 is the factor of p. but it is assumed that p and q are co prime number

Hence our assumption is wrong.

so √3 is irrational number.

Multiplying the rational number with irrational gives irrational number as a result.

17√3 is irrational number.

15 + 17√3 is an irrational number.