Bell Assignment: multiply

1

(2-3\sqrt{6})(-5-\sqrt{6})

1

(5+\sqrt{7})(5-\sqrt{7})

Notes L6-5c: Rationalize Binomial Denominators

note: (a+b)(a-b) are called conjugates. Like [2], when conjugates are multipled together, the middle terms cancel.

Since we are working with square roots, we can use conjugates to eliminate the root.

1

Which is the conjugate of 9-\sqrt{5}?

\sqrt{5}-9

9-\sqrt{5}

9+\sqrt{5}

1

Multiply together 9-\sqrt{5} and its conjugate.

1

Which is the conjugate of -3+\sqrt{11}?

\sqrt{11}-3

\sqrt{11}+3

-3-\sqrt{11}

-3+\sqrt{11}

1

Multiply together -3+\sqrt{11} and its conjugate.

Mathematicians do not like radicals in denominators. So, we rationalize by multiplying by the conjugate.

1

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
you would:

Simplify both the numerator and denominator.
Find the conjugate.
Reduce if possible.
Distibute (by foiling) in both the top and bottom.
Show that you are multipling by the conjugate (on the top and bottom).

1

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
Which step is correct?

\LARGE \frac{-2 (-8+\sqrt{6})}{(-8+\sqrt{6})(-8+\sqrt{6})}

\LARGE \frac{-2 (-8-\sqrt{6})}{(-8+\sqrt{6})(-8-\sqrt{6})}

\LARGE \frac{-2 (-8+\sqrt{6})}{(-8+\sqrt{6})(-8-\sqrt{6})}

\LARGE \frac{-2 (-8-\sqrt{6})}{(-8+\sqrt{6})(-8+\sqrt{6})}

1

Rationalize: \LARGE \frac{-2}{-8+\sqrt{6}}

1

Rationalize: \LARGE \frac{-1}{-2-\sqrt{7}}

1

Rationalize: \LARGE \frac{6}{-8-\sqrt{11}}

1

Rationalize: \LARGE \frac{-2}{-4+\sqrt{14}}

0

Choose all that are true

I am confident in this lesson.

I would like some assistance.

I can find the conjugate.

I can rationalize binomial denominators.

Finish first 14 sections of DelatMath.

113: Operations on Radicals - Rationalize Binomial

Bell Assignment: multiply

113: Operations on Radicals - Rationalize Binomial

Bell Assignment: multiply

(2-3\sqrt{6})(-5-\sqrt{6})

(5+\sqrt{7})(5-\sqrt{7})

Notes L6-5c: Rationalize Binomial Denominators

Which is the conjugate of 9-\sqrt{5}?

Multiply together 9-\sqrt{5} and its conjugate.

Which is the conjugate of -3+\sqrt{11}?

Multiply together -3+\sqrt{11} and its conjugate.

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
you would:

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
Which step is correct?

Rationalize: \LARGE \frac{-2}{-8+\sqrt{6}}

Rationalize: \LARGE \frac{-1}{-2-\sqrt{7}}

Rationalize: \LARGE \frac{6}{-8-\sqrt{11}}

Rationalize: \LARGE \frac{-2}{-4+\sqrt{14}}

Choose all that are true

(2-3\sqrt{6})(-5-\sqrt{6})

(5+\sqrt{7})(5-\sqrt{7})

Notes L6-5c: Rationalize Binomial Denominators

Which is the conjugate of 9-\sqrt{5}?

Multiply together 9-\sqrt{5} and its conjugate.

Which is the conjugate of -3+\sqrt{11}?

Multiply together -3+\sqrt{11} and its conjugate.

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
you would:

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
Which step is correct?

Rationalize: \LARGE \frac{-2}{-8+\sqrt{6}}

Rationalize: \LARGE \frac{-1}{-2-\sqrt{7}}

Rationalize: \LARGE \frac{6}{-8-\sqrt{11}}

Rationalize: \LARGE \frac{-2}{-4+\sqrt{14}}

Choose all that are true

113: Operations on Radicals - Rationalize Binomial

Bell Assignment: multiply

113: Operations on Radicals - Rationalize Binomial

Bell Assignment: multiply

(2-3\sqrt{6})(-5-\sqrt{6})

(5+\sqrt{7})(5-\sqrt{7})

Notes L6-5c: Rationalize Binomial Denominators

Which is the conjugate of 9-\sqrt{5}?

Multiply together 9-\sqrt{5} and its conjugate.

Which is the conjugate of -3+\sqrt{11}?

Multiply together -3+\sqrt{11} and its conjugate.

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}you would:

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}Which step is correct?

Rationalize: \LARGE \frac{-2}{-8+\sqrt{6}}

Rationalize: \LARGE \frac{-1}{-2-\sqrt{7}}

Rationalize: \LARGE \frac{6}{-8-\sqrt{11}}

Rationalize: \LARGE \frac{-2}{-4+\sqrt{14}}

Choose all that are true

(2-3\sqrt{6})(-5-\sqrt{6})

(5+\sqrt{7})(5-\sqrt{7})

Notes L6-5c: Rationalize Binomial Denominators

Which is the conjugate of 9-\sqrt{5}?

Multiply together 9-\sqrt{5} and its conjugate.

Which is the conjugate of -3+\sqrt{11}?

Multiply together -3+\sqrt{11} and its conjugate.

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}you would:

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}Which step is correct?

Rationalize: \LARGE \frac{-2}{-8+\sqrt{6}}

Rationalize: \LARGE \frac{-1}{-2-\sqrt{7}}

Rationalize: \LARGE \frac{6}{-8-\sqrt{11}}

Rationalize: \LARGE \frac{-2}{-4+\sqrt{14}}

Choose all that are true

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
you would:

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
Which step is correct?

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
you would:

To rationalize \LARGE \frac{-2}{-8+\sqrt{6}}
Which step is correct?