Solving Square Root Equations

Front

What is a square root?

Back

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.

Front

How do you solve a basic square root equation?

Back

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

Front

What is the principal square root?

Back

The principal square root is the non-negative root of a number. For example, the principal square root of 16 is 4.

Front

What does it mean to square both sides of an equation?

Back

Squaring both sides of an equation means raising each side of the equation to the power of 2, which can help eliminate square roots.

Front

What is the solution to the equation x^2 = 49?

Back

The solutions are x = 7 and x = -7, since both 7 and -7 squared equal 49.

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What is a perfect square?

Back

A perfect square is an integer that is the square of another integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

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How do you check if a solution to a square root equation is valid?

Back

To check if a solution is valid, substitute it back into the original equation to see if it satisfies the equation.

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What is the domain of a square root function?

Back

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

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What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What is the relationship between square roots and quadratic equations?

Back

Square roots are often used to solve quadratic equations, as squaring both sides can help eliminate the square root and simplify the equation.