Find the value of k in the equation: \( \sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175} \)
Question 1 Report
Find the value of k in the equation: \( \sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175} \)
Answer Details
To find the value of k, we need to isolate the variable on one side of the equation. Let's start by simplifying each of the square roots:
√28 = √4 × √7 = 2√7
√112 = √16 × √7 = 4√7
√175 is already simplified, so we leave it as is.
Now we can substitute these values into the original equation:
2√7 + 4√7 - √k = √175
Simplifying the left side, we get:
6√7 - √k = √175
Next, we'll isolate the radical term by moving the non-radical term to the other side:
6√7 = √k + √175
Squaring both sides to eliminate the radicals:
(6√7)² = (√k + √175)²
36 × 7 = k + 2√k × √175 + 175
252 = k + 5√7√35
252 = k + 5√(7 × 35)
252 = k + 5√(5² × 7)
252 = k + 5 × 5√7
252 = k + 25√7
k = 252 - 25√7
Therefore, the value of k is 252 - 25√7.
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