Radical Operations

Front

What is a radical in mathematics?

Back

A radical is a symbol used to represent the root of a number, most commonly the square root, cube root, etc.

Front

How do you simplify the expression √a - √b?

Back

To simplify √a - √b, you can only combine the terms if a and b are perfect squares or if they can be factored to have a common radical.

Front

What is the product of two square roots, √a and √b?

Back

The product of two square roots is √(a * b).

Front

How do you multiply radicals, such as √a and √b?

Back

To multiply radicals, multiply the numbers inside the radicals and then take the square root of the result: √a * √b = √(a * b).

Front

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

Back

The result is |a|, the absolute value of a.

Front

How do you simplify the expression 3√2 - 3√18?

Back

First, simplify 3√18 to 3 * 3√2 = 9√2. Then, 3√2 - 9√2 = -6√2.

Front

What is the process for simplifying the expression 6√2 ⋅ 5√14?

Back

Multiply the coefficients (6 * 5) and the radicands (√2 * √14) to get 30√(2 * 14) = 30√28 = 60√7.

Front

How do you combine like radicals, such as in the expression 6√3 + 2√75 - 4√27?

Back

First, simplify 2√75 to 10√3 and 4√27 to 12√3. Then combine like terms: 6√3 + 10√3 - 12√3 = 4√3.

Front

What is the distributive property in relation to radicals?

Back

The distributive property allows you to multiply a term outside a radical by each term inside the radical: a(√b + √c) = a√b + a√c.

Front

How do you simplify the expression 2√5(3√3 + 6√2)?

Back

Use the distributive property: 2√5 * 3√3 = 6√15 and 2√5 * 6√2 = 12√10, resulting in 6√15 + 12√10.