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113: Operations on Radicals - Rationalize Binomial

Last updated almost 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

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

1

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

1

Which is the conjugate of -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:

  1. Find the conjugate.
  2. Distibute (by foiling) in both the top and bottom.
  3. Reduce if possible.
  4. Simplify both the numerator and denominator.
  5. 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?

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

Finish first 14 sections of DelatMath.