Operations on 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 simplify √a * √b?

Back

√a * √b = √(a * b).

Front

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

Back

√(a^2) = |a| (the absolute value of a).

Front

How do you add or subtract radicals?

Back

You can only add or subtract radicals with the same index and radicand (e.g., √2 + √2 = 2√2).

Front

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

Back

To simplify √(a * b), factor a and b into their prime factors and simplify any perfect squares.

Front

What is the simplified form of √(12)?

Back

√(12) = √(4 * 3) = 2√3.

Front

How do you simplify 2√5 + 3√5?

Back

2√5 + 3√5 = (2 + 3)√5 = 5√5.

Front

What is the simplified form of √(x^2y)?

Back

√(x^2y) = x√y, assuming x is non-negative.

Front

How do you simplify 4√(3) - 2√(3)?

Back

4√(3) - 2√(3) = (4 - 2)√(3) = 2√(3).

Front

What is the result of √(a^2) + √(b^2)?

Back

√(a^2) + √(b^2) = |a| + |b|.