Simplify:
sqrt(4x^2)/(36y^6)
is the answer x/(3y^3)?
if you mean sqrt [ (4x^2)/(36y^6) ]
then yes
yes it is sqrt [ (4x^2)/(36y^6)]
To simplify the expression sqrt(4x^2)/(36y^6), we can break it down step by step.
Step 1: Simplify the numerator
The numerator is sqrt(4x^2). Since the square root of a square cancels out, sqrt(4x^2) simplifies to 2x.
Step 2: Simplify the denominator
The denominator is 36y^6. To simplify this expression, we can break down both numbers into their prime factors:
36 = 2^2 * 3^2
y^6 = (y^2)^3
Combining these prime factors, we have 36y^6 = 2^2 * 3^2 * (y^2)^3 = 4 * 9 * y^6 = 36y^6.
Step 3: Simplify the expression
Now we can simplify the whole expression by dividing the numerator by the denominator:
2x / 36y^6
To simplify this further, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
(2x / 2) / (36y^6 / 2)
Simplifying further, (2x / 2) simplifies to x, and (36y^6 / 2) simplifies to 18y^6.
Therefore, the simplified expression is x / 18y^6.
So, the answer is x / 18y^6, not x / (3y^3).