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1. WHAT is to be understood by a root ? A power ? The second, third, and

fourth powers ?
2. What is the Index, or Exponent ?
3. What is it to extract the Square Root?
4. Waris the given sum pointed off into periods of two figures each ?
5. In the operation, having found the first figure in the root, why do we subtract

the square number, that is, the square of that figure, from the period in

which it was taken ?
6. Wur do we double the root of a divisor ?
7. In dividing, why do we except the right hand figure of the dividend ?
8. War do we place the quotient figure in the root and also to the right hand ý

the divisor ?
9. If there be decimals in the given number, how must it be pointed ?
10. How is the operation of extracting the Square Root proved ?

1. A CLERGYMAN'S glebe consists of three fields ; the first contains 5
Acr: 2 r. 12 p.the second, 2 ac. 2 r. 15 p. the third 1 ac. 1r. 14 p. in exchange
for which the heritors agree to give him a square field, equal to all the three.
Sought the side of the square ?

Answer 39 Poleş.


IS 2

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3. There is a circle whose diameter is 4 inches, what is the diameter of a circle 4 times as large ?

Answer, 8 inches. Note. SQUARE the given diameter, multiply this square by the given proportion, and the square root of the product will be the diameter required. Do the same in all similar cases.

If the circle of the required diameter were to be less than the circle of the given diameter, by a certain proportion, then the square of the given diameter must have been divided by that proportion.

4. There are two circular ponds in a gentleman's pleasure ground : the diameter of the less is 100 feet, and the greater is three times as large. What Is its diameter.

Answer, 173,9+

5. Ir the diameter of a circle be 12 inches, what will be the diameter of a nother circle, half so large?

Answer, 8,48-inches.

6. A wall is 36 feet high, and a ditch before it is 27 feet wide ; what is the length of a ladder, that will reach to the top of the wall from the opposite side of the ditch ?

Answer, 45 feet.

Note. A FIGURE of three sides, like that formed by the wall, the ditch and the ladder, is called right angled triangle, of which, the square of the hypotenuse, or slanting side, the ladder) is equal to the sum of the squares of the two other sides,that is, the heighth of the wall and the width of the ditch.


7. A LINE of 36 yards will exactly reach from the top of a fort to the opposite bank of a river, known to be 24 yards broad; the height of the wall is required?

Answer, 26,83+ yards.

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