Rationalizing Denominators and Radicals Challenge

This video tutorial covers the properties of radicals, focusing on rationalizing denominators. It explains two methods: 'complete the group' and using conjugates for complex denominators. The tutorial also covers adding and subtracting radicals, emphasizing the need for like terms and simplification. Practical examples are provided for each method, with pauses for viewers to try problems themselves.

What is the process called when you remove a radical from the denominator?

• Rationalizing the denominator

• Simplifying the numerator

• Factoring the denominator

• Completing the square

When rationalizing the denominator using the 'complete the group' method, what do you multiply by?

• The missing factors to complete the group

• The cube of the numerator

• The reciprocal of the denominator

• The square of the denominator

In the example of rationalizing the denominator with an index of 3, what is the final simplified form of cube root of 12 over cube root of 27?

• Cube root of 12 over 27

• Cube root of 3 over 12

• Cube root of 27 over 12

• Cube root of 12 over 3

What is the conjugate of the expression 2 + root 5?

• root 5 + 2

• root 5 - 2

• 2 - root 5

• 2 + root 5

When multiplying by the conjugate, what happens to the middle terms in the denominator?

• They double

• They cancel out

• They become negative

• They remain unchanged

What is the simplified form of the denominator when rationalizing 9 plus square root of 6?

• 81 - 6

• 81 + 6

• 81

• 6

What must be the same in order to add or subtract radicals?

• Only the index

• Only the radicand

• Neither the index nor the radicand

• Both the index and the radicand

In the example of adding radicals, what is the simplified form of 7 times the cube root of 2 minus 4 times the cube root of 2?

• 11 times the cube root of 4

• 3 times the cube root of 4

• 11 times the cube root of 2

• 3 times the cube root of 2

What is the simplified form of the square root of 8?

• 4 root 4

• 4 root 2

• 2 root 4

• 2 root 2

After simplifying, what is the final form of 7 times the square root of 51 plus 35 times the square root of 6?

• 42 times the square root of 6

• 62 times the square root of 6

• 42 times the square root of 51

• 62 times the square root of 51