Is this number a prime factorization number 2^2x3x5^4x8x11^2

Mathematics

2 answers:

melisa1 [442]4 years ago

5 0

(22)(x3)x54x8x112
Simplifies to:
4x757
=4x757
hope it helps

Marta_Voda [28]4 years ago

4 0

2^2 x 3 x 5^4 x 8 x 11^2
= 4 x 3 x 625 x 8 x 121
= 7,260,000

answer is No
The Prime Factorization is:
2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 11 x 11
= 2^5 x 3 x 5^4 x 11^2

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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.