Steven G
Elite Member
- Joined
- Dec 30, 2014
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Prove that if ?∈ℤ such that n^3 is a perfect square, then n is a perfect square
I tried a few things but nothing worked.
Oh, Subhotosh, you want to see some of my work? Sure thing!
For ?∈ℤ, let n^3 be a perfect square. So n^3 = m^2 for some m∈ℤ. Then n = (m1/3)2. Now for n to be a perfect square, we need m1/3∈ℤ. This is where I get stuck. I tried contrapositive but that did not help me.
EDIT: Never mind, this was actually easy to do.
I tried a few things but nothing worked.
Oh, Subhotosh, you want to see some of my work? Sure thing!
For ?∈ℤ, let n^3 be a perfect square. So n^3 = m^2 for some m∈ℤ. Then n = (m1/3)2. Now for n to be a perfect square, we need m1/3∈ℤ. This is where I get stuck. I tried contrapositive but that did not help me.
EDIT: Never mind, this was actually easy to do.
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