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: √(x) = 6. What is x?

Back

x = 36, because squaring both sides gives x = 6² = 36.

Front

Solve: √(x) = -3. What is x?

Back

No solution, because the square root cannot be negative.

Front

What is the solution to the equation √(x + 4) = 2?

Back

x = 0, because squaring both sides gives x + 4 = 2², which simplifies to x = 0.

Front

Solve: √(x - 1) = 5. What is x?

Back

x = 26, because squaring both sides gives x - 1 = 5², which simplifies to x = 26.

Front

What is the first step in solving √(x) = 3?

Back

Square both sides to eliminate the square root, resulting in x = 3².

Front

Solve: √(x + 9) = 3. What is x?

Back

x = 0, because squaring both sides gives x + 9 = 3², which simplifies to x = 0.