Rationalizing a denominator - free math help on homework, 5root(5) / 2root(10)

The video tutorial explains how to simplify a rational expression involving square roots. The instructor begins by addressing the need to eliminate the square root of 10 from the denominator by multiplying both the numerator and denominator by it. The process involves multiplying terms and applying the rule of exponents to combine square roots. The instructor then demonstrates how to simplify the resulting expression further by reducing square root 50 to 5 times square root 2, ultimately arriving at the final simplified form of the expression.

Why is it necessary to multiply both the numerator and the denominator by the square root of 10?

• To change the base of the expression

• To simplify the numerator

• To eliminate the irrational number in the denominator

• To make the expression a whole number

What is the result of multiplying square root 10 by itself?

• 10

• 20

• 5

• 100

Which of the following is a rule of exponents used in the simplification process?

• Multiplying two separate roots allows combining them inside a single root

• Adding two roots results in a single root

• Dividing roots results in a whole number

• Subtracting roots simplifies them

What is the simplified form of square root 50?

• 2 times square root 25

• 25 times square root 2

• 10 times square root 5

• 5 times square root 2

What is the final simplified expression of the given rational expression?

• 5 square root 5 over 4

• 10 square root 2 over 4

• 5 square root 2 over 20

• 5 square root 2 over 4