6.1 - 6.2 Radicals Practice

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, the square root of 4 is represented as √4.

Front

How do you simplify a square root?

Back

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

Front

What is the simplified form of √50?

Back

The simplified form of √50 is 5√2.

Front

What is the simplified form of √60?

Back

The simplified form of √60 is 2√15.

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 square roots?

Back

The sum of two square roots cannot be simplified in the same way as products. For example, √2 + √2 = 2√2, but √2 + √3 remains as is.

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. The square root of a non-perfect square is an example of an irrational number.

Front

How do you convert a radical expression into an exponent?

Back

A radical expression can be converted into an exponent using the property √a = a^(1/2). For example, √x = x^(1/2).

Front

What is the square root of a perfect square?

Back

The square root of a perfect square is an integer. For example, √16 = 4.

Front

What is the relationship between exponents and radicals?

Back

Exponents and radicals are related through the property that a^(m/n) = √[n]{a^m}, where n is the root and m is the power.