Adding and Subtracting 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 (∛). It represents the operation of finding a number that, when multiplied by itself a certain number of times, gives the original number.

Tags

CCSS.8.NS.A.1

Front

How do you simplify the square root of a perfect square?

Back

To simplify the square root of a perfect square, find the number that, when squared, equals the perfect square. For example, √16 = 4 because 4 x 4 = 16.

Front

What is the sum of √3 and √3?

Back

The sum of √3 and √3 is 2√3. When adding radicals with the same index and radicand, you can combine them like like terms.

Front

How do you add √2 and √8?

Back

First, simplify √8 to 2√2. Then, add: √2 + 2√2 = 3√2.

Front

What is the difference between √5 and √20?

Back

First, simplify √20 to 2√5. Then, subtract: √5 - 2√5 = -1√5 or -√5.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

Front

How do you rationalize the denominator of 1/√2?

Back

Multiply the numerator and denominator by √2: (1/√2) * (√2/√2) = √2/2.

Front

What is the product of √3 and √12?

Back

First, simplify √12 to 2√3. Then, multiply: √3 * 2√3 = 2 * 3 = 6.

Front

What is the sum of √5 and 3√5?

Back

The sum is 4√5, as you can combine like terms: √5 + 3√5 = 4√5.

Front

How do you subtract √7 from 2√7?

Back

The result is √7, as you can combine like terms: 2√7 - √7 = 1√7 or √7.