Simplify: √48

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Simplify: √48

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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\(\sqrt{48} = \sqrt{16*3}=\sqrt{16}\sqrt{3}=?\)
4 and 3
its just \(4\sqrt{3}\) the square root of 16 is 4, but the square root of 3 is not so nice so we just write it as sqrt 3

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oooh ok. thank you. i don't understand any of this
To simplify a root like this one, you need to find the greatest factor of 48 that is a perfect square. Here are some whole numbers and their squares: 0 0 1 1 2 4 3 9 4 16 5 25 6 36 Look in the second column. They are the squares of the first 7 whole numbers. One of them is the greatest factor of 48 that is a perfect square. It is 16. Now you rewrite 48 as a product of the greatest perfect square factor and another factor: \(\sqrt {48} = \sqrt { 16 \times 3} \) Next you separate the roots. The product of two roots equals the root of the product. \(= \sqrt{16} \times \sqrt 3\) Finally, you take the square root of 16: \(=4 \times \sqrt 3 = 4\sqrt 3\)

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