Subjects algebra

Square Root 231B10

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1. The problem is to simplify the expression \( \sqrt{x} \), which means finding the principal square root of \( x \). 2. The square root function is defined as \( \sqrt{x} = y \) such that \( y^2 = x \) and \( y \geq 0 \). 3. Important rules: - \( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \) - \( \sqrt{a^2} = |a| \) 4. If \( x \) is a perfect square, say \( x = a^2 \), then \( \sqrt{x} = a \). 5. If \( x \) is not a perfect square, the square root remains as \( \sqrt{x} \) unless further simplification is possible. Final answer: \( \sqrt{x} \)