6 square rot 15y^4* 2 square root 20y^2
6 square rot 15y^4* 2 square root 20y^2
= 6√(15y^2) * √(20y^2) ??
If so, then
= 6y√15 * 2y√5
= 12y^2 √75
= 60y^2 √3
6√(15y^4) * √(20y^2)
...
60√3 y^3
To simplify the expression 6√15y^4 * 2√20y^2, you need to simplify each square root separately and then multiply the simplified expressions.
Let's start by simplifying the square root of 15y^4:
√15y^4
First, express the number 15 as the product of its prime factors:
15 = 3 * 5
Next, simplify the square root of y^4:
√y^4 = y^2
Now, put both parts together:
√15y^4 = √(3 * 5) * y^2
Since the square root is a multiplicative operation, this can be further simplified as:
√15y^4 = (√3 * √5) * y^2
Next, simplify the square root of 20y^2:
√20y^2
Express 20 as the product of its prime factors:
20 = 2 * 2 * 5
Now, simplify the square root of y^2:
√y^2 = y
Combine both parts:
√20y^2 = √(2 * 2 * 5) * y
This can be further simplified as:
√20y^2 = (√2 * √2 * √5) * y
Now that we have simplified both square roots, let's multiply them:
(√3 * √5) * y^2 * (√2 * √2 * √5) * y
Multiplying the like terms within the square roots:
(√3 * √2) * (√5 * √2) * y^2 * y
Simplify the square roots:
√6 * √10 * y^2 * y
Finally, multiply the variables:
√(6 * 10) * y^(2+1)
Simplify 6 * 10:
√60 * y^3
The final simplified expression is:
√60y^3