Which expression is equivalent to sqrt 200

Which expression is equivalent to sqrt 200

The correct answer and explanation is:

The expression equivalent to √200 is:

10√2

✅ Correct Answer: 10√2

🧠 Explanation (Approx. 300 Words)

To simplify the square root of 200, we need to factor 200 into a product of perfect squares and other factors.

Start by finding the prime factorization of 200: 200=2×100=2×102=2×(2×5)2200 = 2 \times 100 = 2 \times 10^2 = 2 \times (2 \times 5)^2

Alternatively: 200=2×100=2×(10)2=2×100200 = 2 \times 100 = 2 \times (10)^2 = 2 \times 100

So, we can break it up: 200=100×2\sqrt{200} = \sqrt{100 \times 2}

Using the property of square roots: a×b=a×b\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}

Apply this to our case: 200=100×2=102\sqrt{200} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}

This is the simplest radical form of √200.

🔍 Why is this useful?

1. Simplified form: Mathematicians prefer expressions in their simplest radical form, as they are easier to use in algebraic equations or comparisons.
2. Computation: If needed, we can approximate √2 ≈ 1.414. So:

10×2≈10×1.414=14.1410 \times \sqrt{2} \approx 10 \times 1.414 = 14.14

This matches the decimal value of √200, which confirms the simplification is correct.

📝 Summary:

• Factor 200 = 100 × 2
• √200 = √100 × √2 = 10√2
• Final answer: 10√2

This process shows how recognizing perfect square factors helps simplify radicals.