Solving by Square roots

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What is the square root of a number?

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The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 x 4 = 16.

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What does it mean to solve an equation by taking square roots?

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Solving an equation by taking square roots involves isolating the variable and then applying the square root operation to both sides of the equation, which can yield two possible solutions (positive and negative).

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What is the principle of squaring both sides of an equation?

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The principle of squaring both sides of an equation states that if two expressions are equal, squaring both sides will maintain the equality, but it may introduce extraneous solutions.

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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 do you check if a solution is valid?

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To check if a solution is valid, substitute the solution back into the original equation to see if both sides are equal.

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What is the relationship between squaring and square roots?

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Squaring a number and taking the square root are inverse operations. Squaring a number gives the area of a square, while taking the square root finds the length of a side of that square.