Solving Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root, cube root, etc. The most common radical is the square root.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors and look for pairs of factors. Each pair can be taken out of the root as a single factor.

Front

What is the square root of 36?

Back

The square root of 36 is 6.

Front

What is the principle of isolating the variable in an equation?

Back

The principle of isolating the variable involves rearranging the equation to get the variable on one side and the constants on the other side.

Front

How do you solve the equation √x = 5?

Back

Square both sides of the equation to eliminate the square root: x = 5^2, which gives x = 25.

Front

What is the solution to the equation x^2 = 25?

Back

The solutions are x = 5 and x = -5.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

Front

How do you solve the equation √(x + 1) = 4?

Back

Square both sides to get x + 1 = 16, then isolate x to find x = 15.

Front

What is the cube root of 27?

Back

The cube root of 27 is 3.

Front

What is the difference between a perfect square and a non-perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer, while a non-perfect square cannot.