Simplifying Radicals: Key Concepts and Techniques

This video tutorial explains how to simplify radicals, focusing on the product and quotient properties of square roots. It covers finding the largest perfect square factor, simplifying variable expressions, and eliminating radicals from denominators. The tutorial provides step-by-step examples to illustrate these concepts, ensuring a comprehensive understanding of simplifying radicals.

What does the product property of square roots state?

• The square root of a product is the sum of the square roots.

• The square root of a product is the product of the square roots.

• The square root of a sum is the sum of the square roots.

• The square root of a sum is the product of the square roots.

How can you simplify the square root of 180 using perfect squares?

• Factor out the square root of 36 and multiply by the square root of 5.

• Divide by the smallest perfect square and subtract from 180.

• Multiply by the smallest perfect square and add to 180.

• Factor out the square root of 49 and multiply by the square root of 4.

How do you simplify the expression 24 times s squared under a square root?

• 4s times the square root of 6

• 2s times the square root of 6

• 2s times the square root of 4

• 6s times the square root of 2

What is the square root of 81/100 simplified?

• 9/10

• 10/9

• 8/11

• 11/8

What is the result of simplifying the square root of 49/64?

• 7/8

• 8/7

• 6/9

• 9/6

How do you simplify the square root of 20/121?

• 2/5 times the square root of 11

• 5/11 times the square root of 2

• 11/2 times the square root of 5

• 2/11 times the square root of 5

What is the simplified form of the square root of 32a/169?

• 4 times the square root of 2a over 13

• 13 times the square root of 2a over 4

• 2 times the square root of 32a over 13

• 13 times the square root of 32a over 4

What is the result of applying the quotient property to the square root of four four-fifths?

• 4 times the square root of 5 over 5

• 5 times the square root of 6 over 5

• 6 times the square root of 5 over 5

• 5 times the square root of 4 over 6

What is the correct way to remove a radical from the denominator?

• Add the radical to the numerator and subtract from the denominator.

• Divide the numerator and denominator by the radical in the denominator.

• Multiply the numerator and denominator by the radical in the denominator.

• Subtract the radical from the numerator and add to the denominator.

What is the simplified form of the square root of 10 times the square root of 16 over the square root of 5?

• 4 times the square root of 2

• 2 times the square root of 4

• 5 times the square root of 16

• 16 times the square root of 10