Simplify: √27 + √3

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Simplify: √27 + √3

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Start by simplifying \(\sqrt{27} \) Can you find two factors of 27, one of which being a perfect square?
so the square root of 30? which would be 10 outside the square root of 3?
Just like in the previous problem, \(\sqrt{48} \), 48 = 16 * 3, and 16 is a perfect square, you can rewrite 27 as the product of two numbers, one of them being a perfect square.

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10√3 so would this be the answer???
No. There is no 30 here. Start with 27. Can you think of two numbers that multiply to 27 from the multiplication tables?
9 and 3
Great. Now what about 9? Is it a perfect square? Is 9 the square of some number?
3 and 3
Exactly. 9 is 3 * 3, or 3^2. Now we can continue with the problem: \(\sqrt{27} + \sqrt 3=\) \(= \sqrt{9 \times 3} + \sqrt 3\) So far we are only showing that 27 = 9 * 3 Ok?
ok
Now we can separate the numbers inside the root. \(= \sqrt{9} \times \sqrt 3 + \sqrt 3\) In the step above, all we did was to separate the root of the product 9 * 3 into the product of the roots of 9 and 3.
yep i see so far.
Now we can easily simplify \(\sqrt 9\) We know that \(\sqrt 9 = 3\), so we write 3 instead of \(\sqrt 9\): \(= 3\sqrt 3 + \sqrt 3\) On the left above you see how \(\sqrt {27} \) simplifies to \(3 \sqrt 3\)
Now we need to do the addition. \(3\sqrt 3 + \sqrt 3\) Is the same as saying "what is 3 square roots of 3 added to 1 square roots of three?"
i understand. but what answer is it?
A. 10√3 B. 27 C. 9√3 D. 4√3
What is 3x + x? What is 3 oranges plus 1 orange?
4 oranges
What is 3 of something plus one of the same thing?
4
Right, so the same way 3 square roots of 3 added to 1 square root of 3 is 4 square roots of 3. Now we can finish the problem. \(= 4 \sqrt 3\)
oh that makes a lot more sense
Here is the whole problem without the explanations in the middle: \(\sqrt{27} + \sqrt 3=\) \(= \sqrt{ 9 \times 3} + \sqrt 3\) \(=\sqrt 9 \times \sqrt 3 + \sqrt 3\) \(= 3\sqrt 3 + \sqrt 3\) \(= 4 \sqrt 3\)
thank you! cane help me with another?
Multiply and simplify: square root of 6 times the quantity of square root of 3 + 5 square root of 2. A. B. C.
You mean this? \(\sqrt 6 \times (\sqrt 3 + 5 \sqrt 2) \)

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