Square Roots and Pythagorean Theorem

The video tutorial explains how to solve a problem using the Pythagorean theorem. It starts by identifying the sides of a right triangle and setting up the equation a² + b² = c². The known values of b and c are substituted into the equation, and the equation is solved to isolate a². The solution involves taking the square root to find the value of a, which is further simplified by breaking down the number 60 into its square root components. The final answer is expressed as 2 times the square root of 15.

What is the side opposite the right angle in a right triangle called?

• Hypotenuse

• Adjacent

• Opposite

• Base

In the given problem, which side is labeled as 'c'?

• 2

• 8

• a

• b

What is the formula for the Pythagorean theorem?

• a + b = c

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b = c^2

If b = 2 and c = 8, what is the equation set up using the Pythagorean theorem?

• a^2 + 2 = 8

• a^2 = 8^2 + 2^2

• a^2 + 8^2 = 2^2

• a^2 + 2^2 = 8^2

What is the next step after setting up the equation a^2 + 4 = 64?

• Add 4 to both sides

• Divide both sides by 4

• Subtract 4 from both sides

• Multiply both sides by 4

After subtracting 4 from both sides, what does a^2 equal?

• 64

• 62

• 56

• 60

What operation is needed to find 'a' from a^2 = 60?

• Square the result

• Take the square root

• Multiply by 2

• Add 60

What is the simplified form of the square root of 60?

• 2√15

• 5√15

• 4√15

• 3√15

Which number is a perfect square that divides 60?

• 25

• 16

• 9

• 4

What is the square root of 4?

• 3

• 4

• 2

• 1