What is the LCM of the numbers 3, 6, and 9? OA. 9 OB. 18 O C. 36 OD 54

Mathematics

2 answers:

Bond [772]3 years ago

8 0

Answer:

b...................................

vaieri [72.5K]3 years ago

5 0

B. 18
:)
explanation: The LCM of 3,6,9 3 , 6 , 9 is the result of multiplying all prime factors the greatest number of times they occur in either number. The LCM of 3,6,9 3 , 6 , 9 is 2⋅3⋅3=18 2 ⋅ 3 ⋅ 3 = 18 .

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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.