simplify the sum of radical expressions: T^2 square root 96tw^2 + 9w square root 6 T^5
Simplify: square root 5w^2 T^7 x square root 20 w^3 T^6
sqrt a * sqrt b = sqrt (a b)
so we have
sqrt ( 5*20*w^5*T^13)
=10 w^2 T^6 sqrt(wT)
To simplify the sum of radical expressions, you need to add or subtract the terms under the radical sign if they have the same radical expression. Let's simplify each term step by step.
Term 1: T^2 √(96tw^2)
First, let's look for any perfect squares in the expression under the square root sign. In this case, 16 is a perfect square that can be factored out from 96. Therefore, we can rewrite the term as follows:
T^2 √(16 * 6 * t * w^2)
Next, we simplify the perfect square:
T^2 * 4w √(6t)
Term 2: 9w √6T^5
This term doesn't have any perfect squares within the radical expression, so it stays the same.
Now, let's add the simplified terms together:
T^2 * 4w √(6t) + 9w √6T^5
Since the terms under the square root sign are different, we cannot combine them. Therefore, the sum of the radical expressions simplifies to:
T^2 * 4w √(6t) + 9w √6T^5