prove that 12√13 is irrational (real numbers)
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prove that 12√13 is irrational (real numbers)
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Answer:
this is solution by given answer.
Step-by-step explanation:
Answer:
root 2+ root 7
root 2+root 7=a (where a is an integer)
squaring both sides
(root 2+root 7)^2=(a)^2
(root 2)^2+(root 7)^+2(root 2)(root 7)=a^2
2+7+2 root 14=a^2
9+2 root 14 =a^2
2 root 14=a^2-9
root 14=a^2-9/2
since a is an integer therefore a^2-9/2 is also an integer and therefore root 14 is also an integer but integers are not rational numbers therefore root 2+root 7 is an irrational number.
proved.
Let us assume that is rational...
Then we get, , where p and q are integers, and q≠0
represents a rational number
Where is irrational. Thus LHS ≠ RHS
our assumption is wrong, is not rational it is Irrational...