Simplifying and Operations with 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.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors, and then pair the factors. Each pair can be taken out of the square root as a single number.

Front

What is the square root of 32?

Back

The square root of 32 can be simplified to 4√2.

Front

How do you multiply two radicals?

Back

To multiply two radicals, multiply the numbers under the radicals together and then simplify the resulting radical if possible.

Front

What is the product of -2√10 and 3√20?

Back

The product is -60√2.

Front

How do you simplify a fraction with a radical in the denominator?

Back

To simplify a fraction with a radical in the denominator, multiply the numerator and denominator by the radical to eliminate the radical from the denominator.

Front

Back

The simplified form is 4√3.

Front

Back

The simplified form is 4√6.

Front

What does it mean to combine like terms in radical expressions?

Back

Combining like terms in radical expressions means to add or subtract terms that have the same radical part.

Front

Back

The simplified form is 5√5 + √3.