Operations with Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, most commonly the square root. It is denoted by the radical sign (√).

Front

What is the square root of a number?

Back

The square root of a number 'x' is a value 'y' such that y² = x. For example, √9 = 3 because 3² = 9.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then simplify by taking out pairs of factors.

Front

What is the product of two square roots?

Back

The product of two square roots can be simplified using the property √a ⋅ √b = √(a*b).

Front

What is the sum of two radicals?

Back

The sum of two radicals can only be simplified if they have the same radicand (the number under the radical). For example, √2 + √2 = 2√2.

Front

What is the difference between like and unlike radicals?

Back

Like radicals have the same radicand, while unlike radicals have different radicands. Only like radicals can be combined.

Front

How do you multiply a radical by a whole number?

Back

To multiply a radical by a whole number, simply multiply the whole number by the coefficient of the radical. For example, 3√2 = 3 times the square root of 2.

Front

What is the simplified form of √18?

Back

The simplified form of √18 is 3√2, since 18 = 9 * 2 and √9 = 3.

Front

What is the value of √(a²)?

Back

The value of √(a²) is |a|, which means the absolute value of 'a'.

Front

How do you add or subtract radicals?

Back

To add or subtract radicals, combine like terms. For example, 2√3 + 3√3 = 5√3.