Prove that root 5 is an irrational number .Hence show that 3 root 5 minus 8 is also an irrational number
tabish1500p7pzip:
what this is 5 minus 8
oh ok
3root5 -8?\
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textbook theorem 1.4: √ 2 on a real number .. page no 12 and
proof: I prove root 5 is an irrational no
let us assume 3√5 -8 is a rational no
3√5-8=a/ b, where a and b are coprime no
3√5=a/b+8
3root5=a/b+8/b
root5 =a+8/3b
LHS is an irrational no......(1)
RHS is a rational no......(2)
1 and 2 as a rational≠irrational no
3√5-8 is not a rational no
∴this contradiction due to our wrong assumption
∴3√5-8 is an irrational no
proof: I prove root 5 is an irrational no
let us assume 3√5 -8 is a rational no
3√5-8=a/ b, where a and b are coprime no
3√5=a/b+8
3root5=a/b+8/b
root5 =a+8/3b
LHS is an irrational no......(1)
RHS is a rational no......(2)
1 and 2 as a rational≠irrational no
3√5-8 is not a rational no
∴this contradiction due to our wrong assumption
∴3√5-8 is an irrational no
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