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A perfect square is a number that can be expressed as the square of an integer. In other words, a number is a perfect square if its square root is an integer.
| Example | Rewrite as a Product | Perfect Square? | Explanation |
|---|---|---|---|
| 25 | 5 * 5 =5^2 | Yes ✓ | 5 is an integer. |
| 30.25 | 5.5 * 5.5 = 5.5^2 | No * | 5.5 is not an integer. |
| 32 | 4sqrt(2) * 4sqrt(2) = (4sqrt(2))^2 | No * | 4sqrt(2) is not an integer. |
| 64 | 8 * 8 =8^2 | Yes ✓ | 8 is an integer. |
Similarly, suppose a variable has an even exponent. In that case, it is still considered a perfect square because this condition guarantees that the variable can be rewritten as the product of two identical powers with integer exponents. y^2 &= y* y x^4 &= x^2 * x^2 z^6 &= z^3 * z^3