If $\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}$, find K

Step 1: Analyze the question We need to simplify each surd and then solve for K.

Step 2: Concept Simplify surds by pulling out perfect squares:

• √50 = √(25 × 2) = 5√2
• √8 = √(4 × 2) = 2√2
• 2/√2 = (2√2)/(√2 × √2) = 2√2/2 = √2 (rationalising the denominator)

Step 3: Solution Substitute into the equation:

5√2 − K(2√2) = √2

Divide every term by √2:

5 − 2K = 1

−2K = 1 − 5 = −4

K = 2

Check: 5√2 − 2(2√2) = 5√2 − 4√2 = √2, which equals 2/√2 = √2 ✓

Step 4: Answer K = 2, which is option D.

Tip: In surd questions, always reduce every surd to the same base (here √2) first. Then you can treat √2 like a common variable and divide it out, which turns the problem into simple algebra.