Radicals 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.

Front

How do you simplify √a*b?

Back

To simplify √a*b, you can separate the radical: √a*b = √a * √b.

Front

What is the simplified form of √48?

Back

The simplified form of √48 is 4√3.

Front

What is the process to simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, pair them, and take the square root of the pairs.

Front

How do you multiply two radicals, such as -2√10 and 3√20?

Back

To multiply two radicals, multiply the coefficients and then multiply the radicands: (-2 * 3) * (√10 * √20) = -6 * √(10*20) = -6 * √200 = -60√2.

Front

What is the simplified form of √275?

Back

The simplified form of √275 is 5√11.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction.

Front

How do you simplify the expression 2√40 - 3√10?

Back

First, simplify √40 to 2√10, then the expression becomes 2(2√10) - 3√10 = 4√10 - 3√10 = √10.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x.