FLASHCARD: Operations with Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, most commonly the square root (√) or cube root (∛).

Front

How do you simplify √a * √b?

Back

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

Front

What is the process to simplify √(a^2 * b)?

Back

√(a^2 * b) = a√b, where a is non-negative.

Front

What is the cube root of a number?

Back

The cube root of a number x is a number y such that y^3 = x.

Front

How do you simplify 3√(a^3)?

Back

3√(a^3) = a * 3√(a) because a^3 can be expressed as a * a * a.

Front

What is the value of √(x^2) for x ≥ 0?

Back

√(x^2) = x.

Front

How do you simplify √(x^4y^2)?

Back

√(x^4y^2) = x^2y.

Front

What is the simplified form of √(a^2b^3)?

Back

√(a^2b^3) = a * b√b.

Front

What is the relationship between radicals and exponents?

Back

Radicals can be expressed as exponents: √x = x^(1/2) and ∛x = x^(1/3).

Front

How do you combine like radicals?

Back

Like radicals can be combined by adding or subtracting their coefficients, e.g., 3√2 + 2√2 = 5√2.