Page:The Algebra of Mohammed Ben Musa (1831).djvu/46

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If you wish to divide twice the root of nine by the root of four, or of any other square^[1], you double the (21) root of nine in the manner above shown to you in the chapter on Multiplication, and you divide the product by four, or by any number whatever. You perform this in the way above pointed out.

In like manner, if you wish to divide three roots of nine, or more, or one-half or any multiple or submultiple of the root of nine, the rule is always the same:^[2] follow it, the result will be right.

If you wish to multiply the root of nine by the root of four,^[3] multiply nine by four; this gives thirty-six; take its root, it is six; this is the root of nine, multiplied by the root of four.

Thus, if you wish to multiply the root of five by the root of ten,^[4] multiply five by ten: the root of the product is what you have required.

If you wish to multiply the root of one-third by the root of a half;^[5] you multiply one-third by a half: it is one-sixth: the root of one-sixth is equal to the root of one-third, multiplied by the root of a half.

If you require to multiply twice the root of nine by

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1. ${\tfrac {2{\sqrt {9}}}{\sqrt {4}}}={\sqrt {\tfrac {36}{4}}}={\sqrt {9}}=3$
2. ${\tfrac {m{\sqrt {p^{2}}}}{\sqrt {q^{2}}}}={\sqrt {\tfrac {m^{2}p^{2}}{q^{2}}}}$
3. ${\sqrt {4}}\times {\sqrt {9}}={\sqrt {4\times 9}}={\sqrt {36}}=6$
4. ${\sqrt {10}}\times {\sqrt {5}}={\sqrt {5\times 10}}={\sqrt {50}}$
5. ${\sqrt {\tfrac {1}{2}}}\times {\sqrt {\tfrac {1}{3}}}={\sqrt {{\tfrac {1}{2}}\times \ {\tfrac {1}{3}}}}={\sqrt {\tfrac {1}{6}}}$