Questions: What is the value of √200 + √50 ? √30 √224 5 √10 15 √2 15 √3

Solution Steps

To solve the expression \(\sqrt{200} + \sqrt{50}\), we need to simplify each square root term separately and then add the simplified forms.

1. Simplify \(\sqrt{200}\) and \(\sqrt{50}\) by expressing them in terms of their prime factors.
2. Combine the simplified forms.

To simplify \(\sqrt{200}\), we factorize 200: \[ 200 = 2^3 \times 5^2 \] Thus, \[ \sqrt{200} = \sqrt{2^3 \times 5^2} = \sqrt{2^2 \times 2 \times 5^2} = \sqrt{(2 \times 5)^2 \times 2} = 10 \sqrt{2} \]

To simplify \(\sqrt{50}\), we factorize 50: \[ 50 = 2 \times 5^2 \] Thus, \[ \sqrt{50} = \sqrt{2 \times 5^2} = \sqrt{5^2 \times 2} = 5 \sqrt{2} \]

Now, we add the simplified forms: \[ \sqrt{200} + \sqrt{50} = 10 \sqrt{2} + 5 \sqrt{2} = (10 + 5) \sqrt{2} = 15 \sqrt{2} \]

Final Answer