Simplifying a radical expression from it's prime factorization

The video tutorial explains the significance of prime factorization in identifying square roots. It covers both long and short methods for prime factorization and highlights when it is necessary. The instructor demonstrates how to simplify expressions by identifying pairs of numbers or variables, showing that the square root of a pair equals the number itself. The final example simplifies an expression to illustrate the process.

Why is prime factorization considered helpful in mathematics?

• It is essential for division.

• It is used to add fractions.

• It simplifies multiplication.

• It helps in identifying square roots.

What is the result of the square root of a number multiplied by itself?

• One

• The square of the number

• Zero

• The number itself

How many pairings can be formed from the expression sqrt(2 * 2) * sqrt(X * X) * sqrt(y * y)?

• Three pairings

• Five pairings

• Two pairings

• Four pairings

What remains inside the square root after simplifying the expression sqrt(2 * 2) * sqrt(X * X) * sqrt(y * y)?

• X and Y

• Nothing

• 2 and X

• 3 and Y

What is the final simplified form of the expression discussed in the video?

• 4Xy * sqrt(3)

• 2Xy * sqrt(3Y)

• 4X^2y * sqrt(3Y)

• X^2y * sqrt(2Y)