Question

Prove that 8-((2×under root7)/3) is an irrational number

Answer 1

Answer:

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let 8-2√7/3 be a rational number and is of the form if p/q where p and q are some integers and qis no equal to 0

so 8-2√7/3 =p/q

=> 8-2√7= 3p/q

=> 8-(3p/q)=2√7

=> 8q-3p/q= 2√7

=> 8q-3p/2q=√7

here 8q ,3p and 2q are intergers

so, 8q-3p/2q is a rational number

but √7 is an irrational number

so our assumption is wrong

=> 8-2√7/3 is an irrational number