Simplifying Fractions with Radicals

The video tutorial explains how to simplify a fraction with a radical in the denominator by multiplying the numerator and denominator by the conjugate of the denominator. It demonstrates the use of distribution and the FOIL method to simplify the expression, ultimately leading to a simplified fraction with no radicals in the denominator.

What is the first step in simplifying a fraction with a radical in the denominator?

• Divide the numerator by the radical

• Subtract the radical from the denominator

• Multiply the fraction by the conjugate of the denominator

• Add the radical to the numerator

Why do we multiply the fraction by the conjugate of the denominator?

• To increase the value of the fraction

• To change the sign of the numerator

• To eliminate the radical from the denominator

• To make the fraction more complex

What is the conjugate of 2 plus root 7?

• Negative 2 plus root 7

• 2 plus root 7

• 2 minus root 7

• Negative 2 minus root 7

What is the result of distributing in the numerator when multiplying by the conjugate?

• 5 plus 10 root 7

• 10 plus 5 root 7

• 10 minus 5 root 7

• 5 minus 10 root 7

What is the result of 2 times negative root 7?

• Positive 2 root 7

• Negative 2 root 7

• Negative root 14

• Positive root 14

What happens to the terms negative 2 root 7 and positive 2 root 7 in the denominator?

• They multiply to root 49

• They cancel each other out

• They add up to root 14

• They remain unchanged

What is the simplified form of 4 minus 7 in the denominator?

• Positive 11

• Negative 11

• Negative 3

• Positive 3

What is the final form of the fraction after changing the sign in the denominator?

• Negative 10 minus 5 root 7 over 3

• 10 minus 5 root 7 over 3

• Negative 10 plus 5 root 7 over 3

• 10 plus 5 root 7 over 3