Adding and Subtracting Radicals

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. For example, √4 represents the square root of 4.

Tags

CCSS.8.NS.A.1

Front

How do you add radicals with the same index and radicand?

Back

To add radicals with the same index and radicand, you simply add their coefficients. For example, (3√6) + (4√6) = (3 + 4)√6 = 7√6.

Front

What is the process for subtracting radicals?

Back

To subtract radicals, you must have the same index and radicand. If they are the same, subtract their coefficients. For example, √18 - √8 can be simplified before subtracting.

Front

How do you simplify √18?

Back

√18 can be simplified by factoring it into √(9*2) = √9 * √2 = 3√2.

Front

What is the simplified form of √8?

Back

√8 can be simplified by factoring it into √(4*2) = √4 * √2 = 2√2.

Front

What is the result of √18 - √8 after simplification?

Back

After simplifying, √18 - √8 = 3√2 - 2√2 = (3 - 2)√2 = 1√2 = √2.

Front

What is the sum of (5√3) + (6√3)?

Back

(5√3) + (6√3) = (5 + 6)√3 = 11√3.

Front

What is the importance of like terms in radical expressions?

Back

Like terms in radical expressions can be combined by adding or subtracting their coefficients, similar to combining like terms in algebra.

Front

How do you combine different radicals, such as 8√2 and 13√3?

Back

Different radicals cannot be combined directly. They remain separate, so 8√2 + 13√3 is the final expression.

Front

What is the principle behind simplifying radicals?

Back

The principle behind simplifying radicals is to express them in their simplest form by factoring out perfect squares or cubes.