A2 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 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^2 = 36

Back

x = 6 or x = -6.

Front

Solve: x^2 = 25

Back

x = 5 or x = -5.

Front

What is the solution to the equation x^2 = 0?

Back

x = 0.

Front

Solve: x^2 - 9 = 0

Back

x = 3 or x = -3.

Front

What is the square root of a negative number?

Back

The square root of a negative number is an imaginary number, represented as 'i' times the square root of the positive value. For example, √(-4) = 2i.

Front

How do you check your solution for a square root equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.