Simplifying Radicals and Cube Roots

The video tutorial explains how to simplify radicals that contain fractions. It covers the simplification of square roots and cube roots by breaking down the numerators and denominators into their perfect square or cube factors. The tutorial demonstrates the process with examples, showing how to rewrite the radicals and simplify them to their simplest form.

What is the first step in simplifying the square root of a fraction?

• Multiply the numerator and denominator by the same number.

• Rewrite the fraction as a product of two fractions.

• Take the square root of the numerator and the denominator separately.

• Add the numerator and the denominator.

Why can the square root of 4/9 be simplified easily?

• Because 4 and 9 are both prime numbers.

• Because 4 and 9 are both odd numbers.

• Because 4 and 9 are both perfect squares.

• Because 4 and 9 are both even numbers.

What is the simplified form of the square root of 4/9?

• 4/5

• 3/4

• 2/3

• 1/2

How is -2 times the square root of 1/121 initially rewritten?

• -2 times the square root of 121/1

• -2 times the square root of 11/11

• -2/1 times the square root of 1/121

• -2/1 times the square root of 11/1

What is the simplified form of -2 times the square root of 1/121?

• -4/11

• -1/11

• -2/11

• -3/11

What is the cube root of 27 simplified to?

• 4

• 3

• 2

• 1

What is the cube root of 125 simplified to?

• 5

• 7

• 6

• 4

Why can the cube root of 27/125 be simplified easily?

• Because 27 and 125 are both prime numbers.

• Because 27 and 125 are both odd numbers.

• Because 27 and 125 are both perfect cubes.

• Because 27 and 125 are both even numbers.

What is the simplified form of the cube root of 27/125?

• 1/2

• 3/5

• 4/5

• 2/3

What is the general approach to simplifying cube roots?

• Add the cube root to itself.

• Multiply the cube root by itself.

• Divide the cube root by a common factor.

• Rewrite the cube root as a product of three equal factors.