Thank you for visiting Is 625 a perfect square If yes what is its root 1 Yes the root of 625 is an integer 2 No the root of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
625 is a perfect square with a square root of 25, an integer. The complex number system encompasses all roots, as exemplified by the fundamental theorem of algebra and factorization of polynomials.So, option 1 is the correct answer.
Explanation:
Yes, 625 is a perfect square because it can be expressed as the product of an integer with itself, specifically 25 times 25. To find the square root of 625, we look for a number that, when multiplied by itself, gives the original number, 625. In this case, the square root of 625 is an integer, which is 25.In mathematics, a perfect square is a number that is the square of an integer. This concept extends to other roots like cube roots, fourth roots, and beyond. The complex number system handles all these roots efficiently, as highlighted by the fundamental theorem of algebra, which states that an nth-order polynomial can be factored completely into n linear factors.
For example, the polynomial x2 + 1, which has no real roots, can be factored into (x - i)(x + i) using complex numbers, where 'i' is the square root of -1. This shows that every polynomial has roots within the complex number system, though those roots are not always real numbers.
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