Understanding Square Root Expressions

The video tutorial explains how to add two square root expressions by simplifying each expression through prime factorization. It covers the prime factorization of 80 and 125, simplifying the square roots, and combining like radicals to achieve a simplified expression. The tutorial emphasizes the importance of understanding perfect square factors and provides a step-by-step approach to solving the problem.

What is the first step in solving the problem of adding two square root expressions?

• Multiply the expressions

• Simplify the square roots

• Divide the expressions

• Add the coefficients

What is the prime factorization of 80?

• 2 x 2 x 2 x 2 x 5

• 2 x 2 x 2 x 5

• 4 x 5 x 4

• 8 x 10

How is x cubed expressed in terms of its factors?

• x x x

• x x x x

• x

• x x

What is the prime factorization of 125?

• 5 x 5

• 5 x 25

• 25 x 5

• 5 x 5 x 5

What is a perfect square factor of 125x?

• 5 squared

• x squared

• 2 squared

• 10 squared

What is the simplified form of 8 times the square root of 2 squared?

• 8 times 3

• 8 times 4

• 8 times 5

• 8 times 2

Why don't we include an absolute value for x in the simplified expression?

• x is less than zero

• x is assumed to be non-negative

• x is a perfect square

• x is a prime number

What is the result of multiplying 4x by the square root of 5 squared?

• 20x

• 16x

• 10x

• 25x

What allows us to add the two expressions together?

• They have different coefficients

• They have like coefficients

• They have different radicals

• They have like radicals

What is the final simplified expression?

• 40x square root 5x

• 20x square root 5x

• 32x square root 5x

• 52x square root 5x