Solving Square Root Equations

Front

What is a square root equation?

Back

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

Front

How do you isolate the square root in an equation?

Back

To isolate the square root in an equation, you can move all other terms to the opposite side of the equation. For example, if you have √x = b + c, you would rearrange it to √x = b + c.

Front

What is the first step in solving a square root equation?

Back

The first step in solving a square root equation is to isolate the square root on one side of the equation.

Front

What do you do after isolating the square root in an equation?

Back

After isolating the square root, you square both sides of the equation to eliminate the square root.

Front

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

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It is important to check your solutions in square root equations because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

Front

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.

Front

How can you solve the equation √(x + 5) = 7?

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To solve √(x + 5) = 7, first square both sides to get x + 5 = 49. Then, subtract 5 from both sides to find x = 44.

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What is the solution to the equation √(x) = 6?

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To solve √(x) = 6, square both sides to get x = 36.

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How do you solve the equation x^2 = 25?

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To solve x^2 = 25, take the square root of both sides, giving x = 5 or x = -5.

Front

What is the domain of a square root function?

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The domain of a square root function is the set of all real numbers x such that the expression under the square root is non-negative (x ≥ 0).