113: Operations on Radicals - Rationalize Binomial

Last updated about 5 years ago

13 questions

1

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113: Operations on Radicals - Rationalize Binomial

Last updated about 5 years ago

13 questions

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

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

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

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

Finish first 14 sections of DelatMath.

Bell Assignment: multiply

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

(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.

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

\sqrt{5}-9

9-\sqrt{5}

9+\sqrt{5}

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

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

\sqrt{11}-3

\sqrt{11}+3

-3-\sqrt{11}

-3+\sqrt{11}

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

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

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

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

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})}

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

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.

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

\sqrt{5}-9

9-\sqrt{5}

9+\sqrt{5}

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

\sqrt{11}-3

\sqrt{11}+3

-3-\sqrt{11}

-3+\sqrt{11}

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

Show that you are multipling by the conjugate (on the top and bottom).

Distibute (by foiling) in both the top and bottom.

Reduce if possible.

Find the conjugate.

Simplify both the numerator and denominator.

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})}

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.

113: Operations on Radicals - Rationalize Binomial

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

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

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

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}}

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

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

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