Algebra

(3*sqrt(x-4))^2

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Identify the expression to simplify

We need to square the entire expression. Squaring means multiplying the expression by itself.
2

Apply the power to each factor

When you raise a product to a power, you apply the exponent to each factor separately. So we square the 3 and square the square root term.
3

Square the constant and the square root

. Now we just need to handle .
4

Simplify the squared square root

Squaring a square root cancels them out: . This works because squaring and square-rooting are inverse operations.
5

Expand the final expression

Distribute the 9: . This is the fully simplified result.

Understanding this problem

Learning Insight

Squaring and square-rooting are inverse operations, so they cancel each other out. This is why . The key rule being used here is , which lets us split the square across the product.

Quick Tip

Whenever you see , just square the constant and drop the square root sign: the answer is always .

Common Mistake

Students often only square the 3 and forget to also square the part, writing instead of .