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

Front

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means to rewrite it in its simplest form, which often involves reducing the radicand (the number inside the radical) and removing any perfect squares.

Front

What is the product of two square roots?

Back

The product of two square roots can be expressed as the square root of the product of the two numbers. For example, √a × √b = √(a × b).

Front

How do you multiply two radicals with the same index?

Back

To multiply two radicals with the same index, multiply the radicands (the numbers inside the radicals) together and keep the same index. For example, √a × √b = √(a × b).

Front

What is the square root of 10 multiplied by the square root of 45?

Back

The square root of 10 multiplied by the square root of 45 simplifies to 15√2.

Front

What is the simplified form of 6√2 ⋅ 5√14?

Back

The simplified form of 6√2 ⋅ 5√14 is 60√7.

Front

What is the result of √3 × √15?

Back

The result of √3 × √15 is 3√5.

Front

What is the product of √5 and √10?

Back

The product of √5 and √10 simplifies to 5√2.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.

Front

How do you identify perfect squares when simplifying radicals?

Back

To identify perfect squares when simplifying radicals, look for factors of the radicand that are perfect squares. For example, in √18, the factor 9 is a perfect square.