Prove the Root 7 is irrational
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Hiii friend,
If possible, let ✓7 is a rational Number and let its simplest form be a/b.
a and b are some integers having no common factor other than 1.
✓7 = a/b.
7 = a²/b² [ ON SWEARING BOTH SIDES].
7b² = a²...........(1)
= 7 divides a²
7 divides a..
LET , a = 7c.
PUTTING THE VALUE OF A IN (1)
7b² = 49c²
b² = 7c²
= 7 divides c²
7 divides c.
Thus,
7 is common factor of a and b.
But ,
This contradicts the fact that a and b have no common factor other than 1.
The contradiction arises by assuming that ✓7 is RATIONAL Number.
HENCE,
✓7 is irrational Number.
HOPE IT HELPS YOU...
If possible, let ✓7 is a rational Number and let its simplest form be a/b.
a and b are some integers having no common factor other than 1.
✓7 = a/b.
7 = a²/b² [ ON SWEARING BOTH SIDES].
7b² = a²...........(1)
= 7 divides a²
7 divides a..
LET , a = 7c.
PUTTING THE VALUE OF A IN (1)
7b² = 49c²
b² = 7c²
= 7 divides c²
7 divides c.
Thus,
7 is common factor of a and b.
But ,
This contradicts the fact that a and b have no common factor other than 1.
The contradiction arises by assuming that ✓7 is RATIONAL Number.
HENCE,
✓7 is irrational Number.
HOPE IT HELPS YOU...
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