Solving Square Root Equations

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What is a square root equation?

Back

A square root equation is an equation that contains a variable within a square root. It can often be expressed in the form √x = a, where x is the variable and a is a constant.

Front

How do you solve a square root equation?

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To solve a square root equation, isolate the square root on one side of the equation and then square both sides to eliminate the square root. Finally, solve for the variable.

Front

What is the principal square root?

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The principal square root of a number is the non-negative root. For example, the principal square root of 25 is 5.

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What does it mean if a square root equation has two solutions?

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If a square root equation has two solutions, it means that squaring the equation resulted in two valid values for the variable that satisfy the original equation.

Front

What is the first step in solving the equation √(x + 3) = 7?

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The first step is to square both sides of the equation to eliminate the square root, resulting in x + 3 = 49.

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What is the importance of checking solutions in square root equations?

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Checking solutions is important because squaring both sides of an equation can introduce extraneous solutions that do not satisfy the original equation.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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How can you determine the number of solutions for a square root equation?

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The number of solutions can be determined by analyzing the equation after squaring both sides. If both sides are equal, there may be two solutions; if one side is greater than the other, there may be no solution.

Front

What is the solution to the equation √(x) = 5?

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The solution is x = 25, obtained by squaring both sides of the equation.

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What is the significance of the radical symbol (√)?

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The radical symbol (√) indicates the square root of a number, representing a value that, when multiplied by itself, gives the original number.