Dividing Radical Expressions 03:37 minutes

Video Transcript

Transcript Dividing Radical Expressions

Meet the man they call Wendelin
the path he takes is bafflin'.
The loyal, royal courier is he,
who expresses himself quite radically.
With no time to wander,
his travels take him yonder,
trundlin' packages for his Lord and Lady.
For a full day,
he travels the way
from Arden to Barton via Circuity.
Taking the long way 'round,
there's sure to be found,
a way shorter than his route currently.
What do I spy?
Is there a new bridge nearby?
Is it really a shortcut, Wendelin wonders.
To figure this out,
and leave no doubt,
we answer questions that divide radical expressions.

Rather than traveling two-thirds of a day to Circuity, to trip trap 'cross the bridge, and then travel an additional one-third of a day from there to Barton, Wendelin can simply cross the new bridge and travel directly from Arden to Barton! How's that, you ask?

The Pythagorean Theorem

Remember the Pythagorean Theorem? ‘a’ squared plus ‘b’ squared is equal to ‘c’ squared. Side 'c' is called the hypotenuse and is the longest side! Using the Pythagorean Theorem to solve for the missing measurement, Wendelin knows how to set up the equation to solve for a positive rational expression, but he needs help simplifying the radical expression.

The Quotient Property of Square Roots

To solve this type of problem, use the Quotient Property of Square Roots: The square root of a quotient is equal to the quotient of the square roots of the numerator and denominator. For all positive real numbers 'a' and 'b' - 'b' does not equal zero. Take a look at how we can apply the quotient property of square roots to solve this problem: The square root of 90 divided by the square root of 10. This is the same as the square root of the fraction 90 over 10. We can simplify this to the square root of 9, and then solve. The quotient is 3, since squaring this number gives you 9.

Let’s try another problem: the square root of the fraction 49 over 9. Hmm, simplifying the fraction won't help, but we can split up the parts and take the square roots. The square root of 49 is equal to 7, and the square root of 9 is equal to 3 giving us 7 over 3. For more complex fractions such as this, note how we separate the coefficients from the radicals, and then apply the quotient property to simplify the square root. The fraction under this radical is simplified to the square root of 4, and the rest is easy.

Getting back to the original problem. Wendelin uses what he’s learned to simplify the radical expression. Using the Quotient Property of Square Roots, the solution is the square root of 5 over 3. Compared to the old route, the new route will save him one-quarter of a day!

Wendelin makes his merry way,
along his newfound pathway
to try out the new overpass.
He notices a troll,
who's blocking his goal,
with a lot of zeal and a lot of sass.
Radical as can be,
Wendelin solves the problems effortlessly,
but tomorrow's another story.