Add, Subtract, Multiply Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you add or subtract radicals?

Back

You can add or subtract radicals only if they have the same index and radicand (the number under the root). For example, √2 + √2 = 2√2.

Front

What is the product of two binomials involving radicals?

Back

To multiply two binomials involving radicals, use the distributive property (FOIL method) and simplify the radicals.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)² is calculated as a² + 2ab + b².

Front

How do you simplify √(a*b)?

Back

√(a*b) = √a * √b, provided a and b are non-negative.

Front

What is the cube root of a number?

Back

The cube root of a number x is a value y such that y³ = x.

Front

How do you simplify expressions with cube roots?

Back

To simplify expressions with cube roots, factor the radicand into perfect cubes and simplify accordingly.

Front

What is the result of (a + b)(a - b)?

Back

The result is a² - b², known as the difference of squares.

Front

How do you combine like terms in radical expressions?

Back

Combine like terms by adding or subtracting the coefficients of the radicals that have the same radicand.

Front

What is the process for rationalizing the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a suitable radical that will eliminate the radical in the denominator.