find root 7 is irrational
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aAnshul11:
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Hii friend,
If possible , let ✓7 be rational and let it's simplest form be A/B.
Now,
✓7 = A/B => 3 = A²/B². [ On squaring both sides]
=> 7B² = A².......(1)
=> 7 Divides A²
=> 7 Divides A.
Let A = 7C for some integer C.
Putting A = 7C in equation (1) we get
7B² = 49C² => B² = 7C²
=> 7 Divides B²
=> 7 Divides B.
Thus 7 is a common factor of A and B.
But this contradicts the fact that A and B have no Common factor other than 1.
The contradicts arises by assuming that ✓7 is rational.
Hence,
✓7 is irrational.
HOPE IT WILL HELP YOU...... :-)
If possible , let ✓7 be rational and let it's simplest form be A/B.
Now,
✓7 = A/B => 3 = A²/B². [ On squaring both sides]
=> 7B² = A².......(1)
=> 7 Divides A²
=> 7 Divides A.
Let A = 7C for some integer C.
Putting A = 7C in equation (1) we get
7B² = 49C² => B² = 7C²
=> 7 Divides B²
=> 7 Divides B.
Thus 7 is a common factor of A and B.
But this contradicts the fact that A and B have no Common factor other than 1.
The contradicts arises by assuming that ✓7 is rational.
Hence,
✓7 is irrational.
HOPE IT WILL HELP YOU...... :-)
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