X^2+16x+64 is the area of a square,find the length of each side of the square.
area=x^2+16x+64=(x+8)^2
so each side is x+8
Ah, we have a mathematical mystery to solve, don't we? Well, let's put on our detective hats and figure it out!
To find the length of each side of the square, we need to use the formula for the area of a square. So, let's rearrange the equation in the form (side length)^2 = area.
Given the equation x^2 + 16x + 64, we can rewrite it as (x + 8)^2 = area.
Therefore, the length of each side of the square is x + 8. Ta-da! Mystery solved! Now, let's move on to the next mathematical adventure, shall we?
To find the length of each side of the square, we have to take the square root of the area given.
Given: Area = x^2 + 16x + 64
Taking the square root of the area:
√(x^2 + 16x + 64)
Now, this expression can be factored as a perfect square:
√((x + 8)^2)
Taking the square root of a perfect square simply gives us the value inside the parentheses:
x + 8
Therefore, the length of each side of the square is x + 8.
To find the length of each side of the square, we need to factorize the given quadratic expression.
The quadratic expression is x^2 + 16x + 64.
To factorize it, we can look for two numbers that multiply to give 64 (the constant term) and add up to give 16 (the coefficient of x).
The numbers that satisfy this condition are 8 and 8.
So, we can rewrite the quadratic expression as (x + 8)(x + 8).
Since the expression represents the area of a square, the side length of the square is equal to the factor that is multiplied twice.
In this case, the factor multiplied twice is (x + 8), so the length of each side of the square is x + 8.
Therefore, the length of each side of the square is x + 8.