Simplifying Square Roots and Radicals

The video tutorial explains how to simplify expressions involving square roots by using prime factorization. It starts with simplifying 5 times the square root of 117 by breaking down 117 into its prime factors and identifying perfect squares. The process involves checking divisibility by smaller numbers and using exponent properties to simplify the expression. Another example is provided with 3 times the square root of 26, demonstrating the process of identifying prime factors and simplifying the expression as much as possible.

What is the first step in simplifying 5 times the square root of 117?

• Multiply 117 by 5

• Check if 117 is a perfect square

• Divide 117 by 2

• Find the prime factorization of 117

How do you determine if 117 is divisible by 3?

• Subtract 3 from 117

• Check if 117 is an even number

• Check if the sum of the digits is divisible by 3

• Divide 117 by 3 directly

What is the result of 117 divided by 3?

• 9

• 27

• 39

• 13

What is the prime factorization of 39?

• 3 x 13

• 3 x 9

• 13 x 13

• 3 x 3

What is the square root of 3 times 3?

• 6

• 9

• 3

• 1

What is the simplified form of 5 times the square root of 117?

• 15√13

• 5√117

• 3√13

• 5√13

What is the first step in simplifying 3 times the square root of 26?

• Check if 26 is a perfect square

• Divide 26 by 3

• Find the prime factorization of 26

• Multiply 26 by 3

What is the prime factorization of 26?

• 2 x 13

• 13 x 13

• 3 x 13

• 2 x 3

Why can't 26 be simplified further?

• It is an even number

• It does not contain any perfect squares

• It is already a perfect square

• It is the product of a perfect square and another number

What is the simplified form of 3 times the square root of 26?

• 6√13

• 3√13

• 3√26

• 3√2