Question

o step by step to reduce the radical., This question page includes a given radical, a line to fill out of the form square root of, input box, end square root, square root of, input box, end square root, and a try button. After pressing the try button, if your answer is correct, it will be added to the page and a new step will appear with another try button. Continue this process until the radical is fully reduced and the submit answer button appears. square root of, 176, end square root 176 ​ square root of, end square root x ​ square root of, end square root x ​

Answer 1

To reduce the radical \(\sqrt{176x}\) step by step, follow these instructions:

### Step 1: Factor the number inside the radical
\[
176 \text{ can be factored into } 16 \times 11
\]

So, we rewrite the radical as:
\[
\sqrt{176x} = \sqrt{16 \times 11 \times x}
\]

### Input for Step 1:
\[
\text{Fill out: } \sqrt{16 \times 11 \times x}
\]

### Step 2: Simplify the square root of the perfect square
\[
\sqrt{16} \text{ is a perfect square and equals } 4
\]
So, we simplify:
\[
\sqrt{16 \times 11 \times x} = 4 \sqrt{11x}
\]

### Input for Step 2:
\[
\text{Fill out: } 4 \sqrt{11x}
\]

### Final Step (end of the process)
At this point, we have fully reduced the radical:
\[
\sqrt{176x} = 4\sqrt{11x}
\]

### Submit Answer:
Your final expression \(4\sqrt{11x}\) can now be submitted.

This concludes the step-by-step process to reduce the radical \(\sqrt{176x}\).