Simplify this expression
sqrt(3y^3)*sqrt(4xy^4)*sqrt(6x^5y^2)
Please show work!!!
√(3y^3)*√(4xy^4)*√(6x^5y^2)
= √(72x^6y^9)
= √(36x^6y^8)*√(2y)
= 6x^3y^4 √(2y)
To simplify the given expression, we can use the properties of square roots. In this case, we need to multiply the individual terms inside the square roots together.
Let's break down the expression and simplify it step by step:
√(3y^3) * √(4xy^4) * √(6x^5y^2)
Step 1: Combine the numbers within each square root:
√(3 * y^3) * √(4 * x * y^4) * √(6 * x^5 * y^2)
Step 2: Simplify the exponents by multiplying them:
√(3 * y * y^2) * √(4 * x * y^4) * √(6 * x^5 * y^2)
Step 3: Simplify the numbers outside the square root by multiplying them:
√(3) * √(y) * √( y^2) * √(4) * √(x) * √( y^4) * √(6 * x^5 * y^2)
Step 4: Simplify the terms under each square root:
√3 * y * y * √4 * x * y^2 * √(6 * x^5 * y^2)
Step 5: Multiply the like terms together:
y^2 * y^2 * x * √3 * √4 * √(6 * x^5 * y^2)
Step 6: Combine the terms outside the square root:
y^4 * x * √(12 * x^5 * y^2)
Now, we can simplify the square root expression further:
√(12 * x^5 * y^2) = √12 * √x^5 * √y^2
Step 7: Simplify the square root of each term:
√12 * √x^5 * √y^2 = 2√3 * x^(5/2) * y
Finally, we can put everything together:
y^4 * x * 2√3 * x^(5/2) * y = 2x^(5/2) * x * y^(4 + 1) * √3 = 2x^(7/2) * y^5 * √3
So, the simplified expression is given by 2x^(7/2) * y^5 * √3.