Solving Equations with Square Roots

Front

What is the definition of a square root?

Back

A square root of a number x is a number y such that y² = x. For example, the square root of 16 is 4, since 4² = 16.

Front

What is the principal square root?

Back

The principal square root of a non-negative number is the non-negative value that, when squared, gives the original number. For example, the principal square root of 25 is 5.

Front

How do you solve the equation x² = a?

Back

To solve the equation x² = a, take the square root of both sides, resulting in x = ±√a.

Front

What is the solution to the equation √x = 4?

Back

To solve √x = 4, square both sides to get x = 4², which simplifies to x = 16.

Front

What is the solution to the equation √x = 9?

Back

To solve √x = 9, square both sides to get x = 9², which simplifies to x = 81.

Front

What are the steps to isolate x in the equation √(x + 3) = 5?

Back

To isolate x, square both sides to get x + 3 = 25, then subtract 3 from both sides to find x = 22.

Front

What is the relationship between squaring and square roots?

Back

Squaring a number and taking the square root are inverse operations. If y = √x, then y² = x.

Front

What is the domain of the square root function?

Back

The domain of the square root function is all non-negative real numbers, as square roots of negative numbers are not defined in the real number system.

Front

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

Back

To check if your solution is correct, substitute the solution back into the original equation and verify if both sides are equal.

Front

What is the solution set for the equation x² = 16?

Back

The solution set for the equation x² = 16 is {4, -4}.