Is This a Sufficient Proof for Perfect Squares with Even Exponents?

In summary, in order for n to be a perfect square, the exponent r must be even. This can be seen when taking the square root of both sides, leaving n equal to p to the power of h, where h is a constant. However, this is not a sufficient proof and the question is not clearly defined as it does not specify what p represents.
  • #1
chaotixmonjuish
287
0
n=p1r1...pkrk

In order for p to be a perfect square, r must be even. Therefore

n=p12h1...pk2hk

taking the square root of both sides I'm just left with

n=p1h1...pkhk

Does this work as a proof that n is a perfect square if r is even? It's a homework problem and I'm not sure if this is sufficient or correct at all.
 
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  • #2
If the p's are distinct primes, it's true the r's must be even for n to be a perfect square, but you haven't proved it. You haven't even stated the problem coherently. What's p?
 

Related to Is This a Sufficient Proof for Perfect Squares with Even Exponents?

What is "Proof of Perfect Squares"?

The proof of perfect squares is a mathematical concept used to determine if a given number is a perfect square or not. A perfect square is a number that can be expressed as the product of two equal integers (e.g. 25 = 5 x 5).

How do you prove a number is a perfect square?

To prove a number is a perfect square, you need to take its square root and check if it is an integer. If the square root is an integer, then the number is a perfect square. For example, to prove 25 is a perfect square, take the square root of 25 which is 5, and since 5 is an integer, 25 is a perfect square.

Can any number be a perfect square?

No, not all numbers are perfect squares. Only numbers that can be expressed as the product of two equal integers are perfect squares. For example, 3 is not a perfect square because it cannot be expressed as the product of two equal integers.

Is there a formula for perfect squares?

Yes, the formula for perfect squares is n^2, where n is the square root of the perfect square. For example, the perfect square of 25 has a square root of 5, so the formula would be 5^2 = 25.

Why is it important to understand the proof of perfect squares?

Understanding the proof of perfect squares is important in many areas of mathematics, such as algebra and geometry. It allows us to quickly determine if a number is a perfect square and simplifies calculations involving perfect squares. It also helps in identifying patterns and relationships between numbers.

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