Gcf of 6x^3, 8x^5, 10x^7

Mathematics

1 answer:

Art [367]2 years ago

5 0

Answer: 2x^3

Step-by-step explanation: Find the prime factors of each term in order to find the GCF (Greatest Common Denominator).

Hope this helps you out! ☺

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What is the following quotient?

seropon [69]

Answer: Choice B) $\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\$

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Work Shown:

$\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\$

This shows why choice B is the answer.

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Explanation:

In the second step, I multiplied top and bottom by $(\sqrt{11}+\sqrt{3})$
This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is $\sqrt{a}-\sqrt{b}$ and you want to rationalize the denominator, then you should multiply top and bottom by $\sqrt{a}+\sqrt{b}$ . The same applies in reverse as well.