Answer:
To solve the square root of 128 in detail, we’ll need to simplify the expression. Let’s break it down step by step:
Simplify the square root of 54xy³:
The square root of 54 can be simplified as the square root of (2² × 3):
√54 = √(2² × 3) = 2√3
The square root of y³ can be separated as the square root of (y² × y):
√y³ = √(y² × y) = y√y
So, the first part of the expression simplifies to 2√3y√y.
Simplify the square root of 128x:
The square root of 128 can be simplified as the square root of (2⁷):
√128 = √(2⁷) = 2³√2
Since there is no y term in this part, we don’t need to further simplify the square root of x.
Therefore, the second part of the expression simplifies to 2³√2x.
Now we can rewrite the original expression with the simplified terms:
√54xy³ - y√128x = 2√3y√y - y(2³√2x)
It’s important to note that we cannot simplify this expression any further because the terms inside the square roots are different (one contains y, while the other contains x) and the bases of the cube roots are also different (one is 3 and the other is 2). Thus, the expression remains as it is.