Find the value of k in the equation: $\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}$

To solve this problem, we need to simplify each square root by expressing the numbers under the radicals as products of perfect squares.

1. Analyze the question

We are given the equation: $\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}$. Our goal is to isolate $\sqrt{k}$ and solve for $k$.

2. Explain the concept

To simplify a square root, we look for the largest perfect square factor (e.g., 4, 9, 16, 25, 36, 49, 64, 81, 100) that divides the number. For example, $\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}$.

3. Show the solution

Step 1: Simplify each radical term.

• $\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}$
• $\sqrt{112} = \sqrt{16 \times 7} = 4\sqrt{7}$
• $\sqrt{175} = \sqrt{25 \times 7} = 5\sqrt{7}$

Step 2: Substitute these back into the original equation. $2\sqrt{7} + 4\sqrt{7} - \sqrt{k} = 5\sqrt{7}$

Step 3: Combine the terms on the left side. $(2 + 4)\sqrt{7} - \sqrt{k} = 5\sqrt{7}$ $6\sqrt{7} - \sqrt{k} = 5\sqrt{7}$

Step 4: Solve for $\sqrt{k}$. Subtract $6\sqrt{7}$ from both sides: $-\sqrt{k} = 5\sqrt{7} - 6\sqrt{7}$ $-\sqrt{k} = -1\sqrt{7}$ $\sqrt{k} = \sqrt{7}$

Step 5: Find $k$. Square both sides of the equation: $(\sqrt{k})^2 = (\sqrt{7})^2$ $k = 7$

4. Identify the answer

Comparing our result to the given options, $k = 7$ matches option B.

5. Exam Tip

When dealing with surds in JAMB, always try to express all terms in the equation in terms of the smallest possible surd (in this case, $\sqrt{7}$). This makes adding and subtracting them as easy as adding simple algebraic terms like $2x + 4x$.