simplify with steps 5(√32)^3
(√32)^3 = 32√32
To simplify the expression 5(√32)^3, we start by simplifying the square root of 32.
1. √32 can be written as √(16 x 2). We break it down into perfect squares.
2. √(16 x 2) = √16 x √2. We can take the square root of each perfect square separately.
3. √16 is equal to 4 since 4 x 4 = 16.
4. Thus, √32 = 4√2.
Now, we substitute 4√2 back into the original expression.
5(4√2)^3
Next, we simplify the cube of 4√2.
5(4√2)^3 = 5(4^3 x (√2)^3)
We simplify the cube of 4, which is 4^3 = 64.
5(64 x (√2)^3)
Finally, we simplify the cube of √2.
(√2)^3 = (√2 x √2 x √2) = 2√2.
Substituting this back into our expression:
5(64 x 2√2)
Let's simplify further:
5(128√2) = 640√2.
Therefore, 5(√32)^3 simplifies to 640√2.