inal answer:
The product of sqrt(5x) is 5x, as multiplying the square root by itself gives the original number under the root, following the properties of exponents and roots in mathematics.
Step-by-step explanation:
The product of sqrt(5x) refers to multiplying the square root of 5x by itself. According to the properties of exponents and roots, when you multiply two of the same roots together, you just get the number under the root. Therefore, sqrt(5x) * sqrt(5x) = 5x. This can also be represented using exponents as (5x)^(1/2) * (5x)^(1/2) = (5x)^(1/2+1/2) = (5x)^1 = 5x.
For a visual example, consider the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (A) is equal to the sum of the squares of the other two sides. If we express this as A = sqrt(Ax^2 + Ay^2), and the lengths of Ax and Ay are 9 and 5, respectively, A would be sqrt(9^2 + 5^2). If you were to calculate that, it would indeed yield the length of the hypotenuse.