Question

The square root of \( \sqrt{50} + \sqrt{48} \) is:

• A. \( 2\sqrt{3} + \sqrt{2} \)
• B. \( 2\sqrt{3} - \sqrt{2} \)
• C. \( 2\sqrt{2} + \sqrt{2} \)
• D. \( 2\sqrt{3} - \sqrt{2} \)

Hint:

To simplify square roots, factor the numbers under the square root and then simplify the expression.

Answer 1

The Correct Option is B

Step 1: Break down the square root expression.
We are given:
\[ \sqrt{50} + \sqrt{48} \] First, simplify the square roots: \[ \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}, \quad \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \] Thus, the expression becomes: \[ 5\sqrt{2} + 4\sqrt{3} \]

Step 2: Square both sides.
Let’s square the expression: \[ (5\sqrt{2} + 4\sqrt{3})^2 = 25 \times 2 + 2 \times 5 \times 4\sqrt{2} \times \sqrt{3} + 16 \times 3 = 50 + 40\sqrt{6} + 48 = 98 + 40\sqrt{6} \] Thus the expression simplifies to: \[ \boxed{2\sqrt{3} + \sqrt{2}} \]