Simplifying Square Roots and Divisibility

This video tutorial explains how to simplify square roots, focusing on their application in the Pythagorean theorem. It covers the process of breaking down numbers into prime factors and using pairs to simplify radicals. Several examples, including radicals 27, 18, 216, and 144, are provided to illustrate the method. The video also demonstrates how to apply simplified radicals in solving the Pythagorean theorem, emphasizing the importance of leaving answers in radical form rather than decimals.

Why is it important to leave answers in simplest radical form?

• To avoid decimals in the final answer

• To make the answer look more complex

• To ensure accuracy in calculations

• To avoid using calculators

What is the invisible number outside a square root called?

• A square root

• A square

• A cube root

• A prime factor

How can the square root of 27 be simplified?

• By using a calculator

• By adding the digits

• By dividing by 9

• By finding pairs of prime factors

What is the simplified form of √18?

• 9√2

• 6√3

• 3√2

• 2√3

Which trick helps determine if a number is divisible by 3?

• Check if it's even

• Add the digits and see if the sum is divisible by 3

• Subtract 1 from the number

• Divide by 2

What is the simplified form of √216?

• 6√6

• 9√4

• 12√3

• 3√12

What indicates that a number is a perfect square?

• It is divisible by 5

• It ends with a 0

• All prime factors can be paired

• It is an even number

What is the simplified form of √144?

• 16

• 12

• 10

• 14

Why use radicals in the Pythagorean theorem?

• To make calculations easier

• To use a calculator

• To avoid decimals

• To find exact values

In a right triangle, what does the hypotenuse represent?

• The side adjacent to the right angle

• The side opposite the right angle

• The shortest side

• The longest side