sqrt(k) = 300 div 15What is the value of k in the equation above?20404008,000

1. SIMPLIFY the right side of the equation

• Given equation: \(\sqrt{\mathrm{k}} = 300 \div 15\)
• First, calculate the division: \(300 \div 15 = 20\)
• The equation now becomes: \(\sqrt{\mathrm{k}} = 20\)

2. INFER the solution strategy

• To find k when we have \(\sqrt{\mathrm{k}} = 20\), we need to "undo" the square root
• The inverse operation of taking a square root is squaring
• Strategy: Square both sides of the equation

3. SIMPLIFY by applying the squaring operation

• Square both sides: \((\sqrt{\mathrm{k}})^2 = (20)^2\)
• The left side simplifies to k (since squaring undoes the square root)
• The right side gives us: \(20^2 = 400\)
• Therefore: \(\mathrm{k} = 400\)

Answer: C) 400

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may not recognize that they need to square both sides to solve the equation. Instead, they might think that since \(\sqrt{\mathrm{k}} = 20\), then \(\mathrm{k}\) must also equal 20.

This reasoning leads them to select Choice A (20) without performing the necessary squaring step.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly understand the approach but make arithmetic errors. They might miscalculate \(300 \div 15\) as something other than 20, or they might incorrectly compute \(20^2\) (perhaps getting 40 instead of 400).

An error like thinking \(20^2 = 40\) would lead them to select Choice B (40).

The Bottom Line:

This problem tests whether students understand the relationship between square roots and squaring as inverse operations, combined with careful arithmetic execution. Success requires both strategic thinking about how to isolate the variable and precise calculation skills.