Week 2 – Precalculus 11

Entire and Mixed Radicals

this week in math we learned about Entire and Mixed radicals and how to switch between the two along with reviewing our squares and cubes.

Entire Radicals

Entire radicals are composed of only a single number under the radical and no number beside the radical another way of saying it is the way that we have seen a number under a square root up until now. Entire Radicals tend to look more nice but aren’t as easy to calculate with. ex: \sqrt{64}

Mixed radicals

Mixed radicals tend to be easier to multiply or generally do math with. Mixed radicals look similar to how mixed fractions look like, with that they each have a base (the big number outside the fraction or radical) but the difference between a mixed radical and a mixed fraction is that with a mixed fraction the base (depending on the situation but for this example we shall use 1 \frac{1}{2} ) would be worth the total of the denominator, meaning that the 1 in 1 \frac{1}{2} if turned into an improper fraction would be \frac{3}{2}, But for a mixed radical there is no base but in fact a coefficient which would multiply the root of said number. EX: 2 \sqrt{24} would need to be turned into \sqrt{4} \cdot \sqrt{24} to be able to easily multiply the radicals together and once we multiply both radicals we should get an entire radical in the end \sqrt{4} \cdot \sqrt{24} = \sqrt{96} and to turn an entire radical to a mixed radical you would need to figure out which square times another number gives me the number that you would have in this situation it’s 96. And then proceed to reduce the square into a coefficient to turn it into a Mixed radical.

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