sqrt 15y * 3 sqrt 81y
Simplify the radical expression
My answer is 27 sqrt 15y^2
My answer is 27 sqrt 15y^2
yes that is correct
sorry copied answer wrong 27y sqrt 15
Well, I have to admit that you took a pretty radical approach to solving that problem! But I'm afraid that your answer is not quite right. Let me take a stab at it.
When you multiply the square root of 15y by 3 times the square root of 81y, you can simplify it further. The square root of 81 is 9, and the square root of y times y is just y. So, we have 3 times 9 times the square root of 15 times y.
That simplifies to 27 times the square root of 15y. So, your final answer is 27 sqrt(15y). Great effort though! Keep up the mathematical comedy routine!
To simplify the radical expression:
The first step is to rewrite each square root as a power. The square root of 15y can be written as (15y)^(1/2), and the square root of 81y can be written as (81y)^(1/2).
Next, apply the properties of exponents. When multiplying two expressions with the same base, you can add their exponents.
(15y)^(1/2) * 3 * (81y)^(1/2)
= 3 * (15y)^(1/2) * (81y)^(1/2)
Now, simplify each square root separately:
(15y)^(1/2) = √(15y) = √15 * √y = √(3^2 * 5 * y) = 3√(5y)
(81y)^(1/2) = √(81y) = √81 * √y = 9√(y)
Substitute these simplified square roots back into the expression:
3 * (15y)^(1/2) * (81y)^(1/2)
= 3 * (3√(5y)) * (9√(y))
= 3 * 3 * 9 * √(5y) * √(y)
= 27 * √(5y) * √(y)
= 27 * √(5y^2)
= 27√(5y^2)
So the simplified radical expression is 27√(5y^2).