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Taking the n th Root to Solve Equations

In Chapter 7.1, we revisit the method of solving quadratic equations by taking the square root of both sides. This technique is applied in examples such as x² = 49, (x – 1)² = 64, and 3x² = 27. To solve these equations, isolate the variable or expression raised to a power and take the nth root of both sides. If the exponent is even, remember to consider both the positive and negative roots (±). Continue isolating the variable if needed. This method equips readers with the necessary skills to tackle various quadratic equations.

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Taking the n th Root to Solve Equations

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  1. Taking the nth Root to Solve Equations Chapter 7.1

  2. Recall: Solving Quadratic Equations by Taking the Square Root of Each Side Examples: Solve each equation. • x2 = 49 • (x – 1)2 = 64 • 3x2 = 27

  3. Taking the nth Root of each side • Isolate the variable or expression being raised to a power • The exponent is n, take the nthroot of both sides of the equation (use a calculator). • If n is even, remember your variable could be positive or negative (you need ± sign). • If an expression was being raised to a power, continue to isolate variable.

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