Solving Square Root Equations

Front

What is a square root?

Back

A square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

Front

How do you solve a square root equation?

Back

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.

Front

What is the principal square root?

Back

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

Front

What does it mean if a square root equation has no solution?

Back

A square root equation has no solution if the expression under the square root (the radicand) is negative, as square roots of negative numbers are not real.

Front

Solve: x² = 36

Back

x = 6 or x = -6.

Front

Solve: x² = 25

Back

x = 5 or x = -5.

Front

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 radicand is non-negative (x ≥ 0).

Front

Solve: √(x + 4) = 6

Back

x + 4 = 36, so x = 32.

Front

Solve: √(x - 1) = 5

Back

x - 1 = 25, so x = 26.

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).