Simplifying Radical Expressions with Fractions

This video tutorial covers simplifying radical expressions, focusing on those with fractions. It explains the conditions for a radical expression to be in its simplest form and demonstrates the process through various examples, including square roots and cube roots, with and without variables. The tutorial also covers rationalizing denominators and the use of absolute values when dealing with variables.

Which of the following is NOT a condition for a radical expression to be in its simplest form?

• No radical contains a fraction.

• All possible nth powered factors have been removed from each radical.

• The numerator of a fraction contains a radical.

• No denominator of a fraction contains a radical.

What is the first step in simplifying the square root of 4/9?

• Remove the fraction from under the radical.

• Multiply the numerator and denominator by a radical.

• Break it into the square root of the numerator and the square root of the denominator.

• Combine the numerator and denominator under one radical.

Why does the square root of 4/9 simplify perfectly?

• Because 4 and 9 are both perfect squares.

• Because 4 and 9 are both prime numbers.

• Because 4 and 9 are both even numbers.

• Because 4 and 9 are both odd numbers.

What is the simplified form of the square root of 9/11?

• 3 square root of 11 divided by 11

• Square root of 9 divided by 11

• Square root of 9 divided by square root of 11

• Square root of 11 divided by 3

What is the purpose of multiplying both the numerator and denominator by the square root of 11 in the example of 9/11?

• To make the denominator a perfect square.

• To make the fraction a whole number.

• To make the numerator a perfect square.

• To remove the fraction from under the radical.

What is the first step in simplifying the cube root of 2/3?

• Remove the fraction from under the radical.

• Multiply the numerator and denominator by the cube root of 3.

• Break it into the cube root of the numerator and the cube root of the denominator.

• Combine the numerator and denominator under one radical.

Why do we multiply both the numerator and denominator by the cube root of 3x3 in the example of 2/3?

• To make the denominator a perfect cube.

• To remove the fraction from under the radical.

• To make the numerator a perfect cube.

• To make the fraction a whole number.

In the example with variables, what is the first step in simplifying the square root of 2 divided by 5x squared y cubed?

• Combine the numerator and denominator under one radical.

• Remove the fraction from under the radical.

• Break it into the square root of the numerator and the square root of the denominator.

• Multiply the numerator and denominator by the square root of 5.

When simplifying radicals with variables, when do we need to include the variable part in an absolute value?

• When the index is even and the simplified variable has an even exponent.

• When the index is even and the simplified variable has an odd exponent.

• When the index is odd and the simplified variable has an even exponent.

• When the index is odd and the simplified variable has an odd exponent.

What is the simplified form of the cube root of 5 divided by 4x squared y?

• Cube root of 10xy divided by 2xy squared

• Cube root of 10xy squared divided by 2xy

• Cube root of 5 divided by 4xy

• Cube root of 5 divided by 2xy squared