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Examples for FRActice.

1. It is required to find the difference of 2/50 and v18.

2. It is required to find the difference of 3/320 and 3/40.

3. It is required to find the difference of v. and V ;

4. It is required to find the difference of 2./4 and v8. 5. It is required to find the difference of 33/4 and 3/72.

6. It is required to find the difference of v; and vi.

7. It is required to find the difference of v30aoz and v/200***.

8. It is required to find the difference of 8vao and avao. **

CASE WI.

To multiply surd quantities together.

RULE,

When the surds are of the same kind, find the product of the rational parts, and the product of the surds, and the two joined together, with their common radical sign between them, will give the whole product required; which may be reduced to its most simple form by Case III.

But if the surds are of different kinds, they must be reduced to a common index, and then multiplied together as usual.

It is also to be observed, as before mentioned, that the product of different powers, or roots, of the same quantity, is found by adding their indices.

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ExAMPLES.

1. It is required to find the product of 3 V8 and 2v3. Here 3 V8 Multiplied 2 v 6

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Whence (72) + Ans. 4. It is required to find the product of 5va and 33/a.

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5. It is required to find the product of 5 V8 and 3 v 5, 6. It is required to find the product of 3, 18 and 5 & 4. * ~ 7. Required the product of #ve and ove.

8. Required the product of #vis and 5v20. 9. Required the product of 2V3 and 134 y5. • 10. Required the product of 7214; and 120,03 11. Required the product of 4+2,22 and 2–v2. 12. Required the product of (a+b)+ and (a + b);

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When the surds are of the same kind, find the quotientiof the rational parts, and the quotient of the surds, and the two joined together, with their common radical sign between them, will give the whole quotient required. But if the surds are of different kinds, they must be reduced to a common index, and then be divided as be

fore. It is also to be observed, that the quotient of different

powers or roots of the same quantity, is found by subtracting their indices.

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10. It s required to divide 32.7 a by 13; va

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12. It is required to divide v20+-v12 by v5A/+3. .Note. Since the division of surds is performed by subtracting their indices, it is evident that the denominator of any fraction may be taken into the numerator, or the numerator into the denominator, by changing the sign of its index.

wn Also, since : = 1, or = a”=a", it follows, that the d expression a' is a symbol equivalent to unity, and, con

sequently, that it may always be replaced by 1 whenever it occurs. (t)

(t) To what is above said, we may also farther observe, 1. That 0 added to or subtracted from any quantity, makes it neither greater nor less ; that is,

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1 - - 3. Let as be expressed with a negative index.

-l. - - - - 4. Let a * be expressed with a positive index.

5.

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Let — be expressed with a negative index.
a-Ha. p I negative index

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a 4-0=a, and a-0=a. 2. Also, if nought be multiplied or divided by any quantity; both the product and quotient will be nought; because any number of times 0, or any part of 0, is 0; that is,

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3. From this it likewise follows, that nought divided by nought, is a finite quantity, of some kind or other.

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4. Farther, if any finite quantity be divided by 0, the quotient will be infinite.

For let 1-4. then, if b remains the same, it is plain, the less a

is, the greater will be the quotient g; whence, if a be indefinitely small, a will be indefinitely great ; and consequently, when a is 0, the quotient q will be infinite : that is, %, or -- . Which properties are of frequent occurrence in some of the higher parts of the science, and should be carefully remembered.

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