Simplifying Square Roots and Radicals

The video tutorial covers simplifying radicals with fractions, focusing on identifying perfect squares and rationalizing denominators. It provides multiple examples, starting with basic simplifications and progressing to more complex problems. The instructor emphasizes the importance of writing out steps to verify work and introduces techniques for rationalizing denominators. The session concludes with practice problems to reinforce the concepts learned.

What is the first step in simplifying the square root of 98 over 2?

• Divide 98 by 2.

• Multiply 98 by 2.

• Check if 2 is a perfect square.

• Check if 98 is a perfect square.

When simplifying the square root of 7 over 16, why can the expression be separated?

• Because neither 7 nor 16 is a perfect square.

• Because both 7 and 16 are perfect squares.

• Because 16 is a perfect square.

• Because 7 is a perfect square.

What does rationalizing the denominator involve?

• Multiplying the numerator by 2.

• Removing the square root from the denominator.

• Adding a square root to the numerator.

• Dividing the denominator by 2.

In the expression square root of 4x squared over 36x, which part is not a perfect square?

• x

• x squared

• 36

• 4

How do you simplify the square root of 5 over 20?

• Simplify the fraction first.

• Separate the square root of 5 and 20.

• Add 5 to the numerator.

• Multiply both by 5.

What is the simplified form of the square root of 45 over 4?

• 3 square root of 5 over 4

• Square root of 5 over 2

• Square root of 45 over 2

• 3 square root of 5 over 2

What is the first step in rationalizing the denominator of square root of 75 over 2?

• Multiply the numerator by 2.

• Add 2 to the denominator.

• Multiply the denominator by 75.

• Simplify the numerator.

What is the result of multiplying the square root of 2 by itself?

• 2

• Square root of 4

• 4

• Square root of 2

Why is it important to write out all steps when simplifying radicals?

• To ensure accuracy and check work.

• To avoid using a calculator.

• To make it look complicated.

• To save time.

What is the simplified form of the square root of 1 over 4?

• 4 over 1

• 1 over 4

• 2 over 1

• 1 over 2