Exploring Special Right Triangles and Rationalizing Denominators

What are the two types of special right triangles discussed?

• 30-60-90 and 45-45-90

• 30-45-105 and 60-30-90

• 30-30-120 and 60-60-60

• 45-45-90 and 90-90-0

Why is rationalizing the denominator necessary in mathematics?

• To make the expression look simpler

• To remove the square root from the denominator

• To ensure the denominator is a whole number

• To convert the fraction into a decimal

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

• Square root of 4

• 4

• 2

• Square root of 2

What does rationalizing the denominator involve?

• Multiplying the numerator by the square root

• Dividing the denominator by the square root

• Adding the square root to both the numerator and denominator

• Multiplying both the numerator and denominator by the same square root

What is the purpose of multiplying by the square root of 2 over the square root of 2?

• To simplify the fraction

• To create an equivalent fraction of 1

• To eliminate the square root from the numerator

• To double the value of the fraction

In a 45-45-90 triangle, if the hypotenuse is 8, what is the length of one leg?

• 8 times the square root of 2

• 4

• 2 times the square root of 2

• 4 times the square root of 2

How is the hypotenuse of a 45-45-90 triangle related to its legs?

• It is the length of one leg times the square root of 2

• It is double the length of one leg

• It is half the length of one leg

• It is equal to one leg

How do you find the missing side lengths in a 30-60-90 triangle?

• Dividing by the square root of 3

• Using Pythagoras theorem

• Adding the square root of 3

• Multiplying by the square root of 3

What is the hypotenuse of a 30-60-90 triangle if the short leg is 5 times the square root of 3?

• 10

• 10 times the square root of 3

• 15 times the square root of 3

• 5 times the square root of 6

In a 45-45-90 triangle, if one leg is 5 times the square root of 3, what is the hypotenuse?

• 10 times the square root of 3

• 5 times the square root of 6

• 5 times the square root of 2

• 10