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. For example, √2 represents the square root of 2.

Front

How do you simplify √a * √b?

Back

√a * √b = √(a * b). For example, √2 * √3 = √(2 * 3) = √6.

Front

What is the product of (a√b)(c√d)?

Back

(a√b)(c√d) = ac√(bd). For example, (3√2)(2√3) = 6√(2*3) = 6√6.

Front

How do you simplify a√b - c√b?

Back

a√b - c√b = (a - c)√b. For example, 5√2 - 3√2 = (5 - 3)√2 = 2√2.

Front

What is the area of a rectangle with length l and width w expressed in radicals?

Back

Area = l * w. If l = 3√2 and w = 2√3, then Area = 3√2 * 2√3 = 6√6.

Front

How do you simplify √(a^2)?

Back

√(a^2) = |a|. For example, √(4) = 2 and √(x^2) = |x|.

Front

What is the result of 3√2 - 3√18?

Back

3√2 - 3√18 = 3√2 - 3(3√2) = 3√2 - 9√2 = -6√2.

Front

What is the product of 6√2 and 5√14?

Back

6√2 * 5√14 = 30√(2*14) = 30√28 = 60√7.

Front

How do you simplify √(a/b)?

Back

√(a/b) = √a / √b. For example, √(4/9) = √4 / √9 = 2/3.

Front

What is the simplified form of (3√6)(2√3)?

Back

(3√6)(2√3) = 6√(6*3) = 6√18 = 18√2.