Perfect Square Factors and Simplifying Expressions

The video tutorial explains how to simplify expressions involving square roots by identifying perfect square factors. It covers breaking down radicands into perfect squares, simplifying expressions, and combining like radicals to achieve a simplified form. The tutorial concludes with a final simplified expression.

What is the first step in simplifying square roots?

• Identify the radicands

• Multiply the radicands

• Divide the radicands

• Identify perfect square factors

Which of the following is a perfect square factor of 32?

• 4

• 16

• 8

• 2

How can y to the 11th be expressed to identify a perfect square factor?

• y to the 11th is already a perfect square

• y to the 11th as y to the tenth times y

• y to the 11th as y to the fifth times y to the fifth times y

• y to the 11th as y to the sixth times y to the fifth

Which of the following is a perfect square factor of x to the ninth?

• x to the sixth

• x to the seventh

• x to the eighth

• x to the ninth

What is the perfect square factor of y to the 16th?

• y to the 15th

• y to the 14th

• y to the 16th

• y to the 8th

How is x to the fourth expressed as a perfect square factor?

• x squared times x squared

• x cubed times x

• x to the fourth is already a perfect square

• x to the fifth times x

What is the result of simplifying the square root of 16?

• 16

• 4

• 2

• 8

What is the simplified form of the expression after combining like radicals?

• 8 x cubed y to the fifth square root two y plus five x to the fourth y to the eighth square root two x

• 8 x cubed y to the fifth square root two x plus five x to the fourth y to the eighth square root two y

• 8 x cubed y to the fifth square root two x minus five x to the fourth y to the eighth square root two y

• 8 x cubed y to the fifth square root two y minus five x to the fourth y to the eighth square root two x

What is the result of adding four x cubed y to the fifth with another four x cubed y to the fifth?

• Four x cubed y to the fifth

• Eight x cubed y to the fifth

• Sixteen x cubed y to the fifth

• Twelve x cubed y to the fifth

What is the final simplified expression?

• Eight x cubed y to the fifth square root two x minus five x to the fourth y to the eighth square root two y

• Eight x cubed y to the fifth square root two x plus five x to the fourth y to the eighth square root two y

• Eight x cubed y to the fifth square root two y minus five x to the fourth y to the eighth square root two x

• Eight x cubed y to the fifth square root two y plus five x to the fourth y to the eighth square root two x