Question

prove that 4-3√7 is an irrational number where √7 is irrational​

Answer 1

Answer:

HENCE PROVED

Step-by-step explanation:

As we know that sum, difference, product and quotient of a rational(4) and irrational(3 root7) number is always irrational.

And root7 is a non-terminating non-recurring(repeating) decimal expansion.

Answer 2

Step-by-step explanation:

let 4-3√7 is rational number

since 4-3√7 ,=p/q

3√7=p/q-4

3√7=p-4q/q

√7=p-4q/3q

since p/q is rational number

hence p-4q/3q is also a rational number

therefore √7 is also a rational number

but we have given that √7 is an irrational number

so this contradiction our assumption

therefore 4-3√7 is irrational number

HENCE proved/

hope this helps you