Question 6 simplified expression by subtracting the radicals blank radical 50 - 2 radical 8 equals

1 answer

To simplify the expression \( \sqrt{50} - 2\sqrt{8} \), we start by simplifying each radical term.

  1. Simplify \( \sqrt{50} \): \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \]

  2. Simplify \( 2\sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] Therefore, \[ 2\sqrt{8} = 2 \cdot 2\sqrt{2} = 4\sqrt{2} \]

Now, substitute these simplified forms back into the original expression: \[ \sqrt{50} - 2\sqrt{8} = 5\sqrt{2} - 4\sqrt{2} \]

Now combine like terms: \[ 5\sqrt{2} - 4\sqrt{2} = (5 - 4)\sqrt{2} = 1\sqrt{2} = \sqrt{2} \]

Thus, the simplified expression is: \[ \sqrt{2} \]