Video: Simplifying Numerical Expressions Using Properties of Conjugates of Irrational Numbers

Simplify (12√5 − 23)/13√5 by rationalizing the denominator.

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Video Transcript

Simplify 12 root five minus 23 divided by 13 root five by rationalizing the denominator.

In order to rationalize the denominator, we must multiply the fraction by root five. We must multiply the numerator by root five and the denominator by root five. Whatever you do to the top, you must do to the bottom of a fraction.

If we consider the numerator first, we need to multiply root five by 12 root five minus 23. Root five multiplied by 12 root five is the same as 12 multiplied by five, as root five multiplied by root five is five. 12 multiplied by five is equal to 60.

The second part of this calculation involves multiplying root five by negative 23. This gives us negative 23 root five. Therefore, root five multiplied by 12 root five minus 23 is equal to 60 minus 23 root five. If we then consider the denominator of the fraction, we need to multiply 13 root five by root five.

As root five multiplied by root five is equal to five, this gives us 13 multiplied by five, which is equal to 65. Therefore, the simplified version of our fraction, 12 root five minus 23 divided by 13 root five, is 60 minus 23 root five divided by 65.

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