5. What is the fquare root of 964,5192360241 ?

9. What is the square root of 1030892198,4001 ?

Supplement to the Square foot.

QUESTIONS.

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

and fourth powers?

2. What is the Index, or Exponent?

3. What is it to extract the Square Root?

4. Why is the given fum 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. Why do we double the root of a divifor?

7. In dividing why do we except the right hand figure of the dividend ?

8. Why do we place the quotient figure in the root and alfo to the right hand of the divifor?

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?

EXERCISES IN THE SQUARE ROOT.

1. A Clergyman's glebe confifts of three fields; the firft contains 5 Aer. 2r. 12 p. the fecond, 2 ac. 2 r. 15 p the third 1 ac. 1 r. 14 p. in exchange for which the heritors agree to give him a square field equal to all the three. Sought the fide of the fquare? Ans. 39 poles.

2. A General has an army of 4096 men; how many must he place in rank and file to form them into a fquare?

Answer 64.

3. There is a circle whofe diameter is 4 inches, what is the diameter of a circle 4 times as large ? Ans. 8 inches.

NOTE. Square the given diamet, multiply this fquare by the given proportion, and the fquare root of the product will be the diameter required. Do the fame in all fimilar cafes.

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

g ven

What

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

Ans. 178,2+

5. If the diameter of a circle be 12 inches, what will be the diameter of another circle, half fo large?

Ans. 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 oppofite fides of the ditch?

Anfwer 45 feet.

NOTE. A Figure of three fides, like that formed by the wall, the ditch and the ladder is called a right angle triangle, of which, the fquare of the hypotenuse, or flanting fide, (the ladder) is equal to the fum of the fquares of the two other fides, 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 oppofite bank of a river, known to be 24 yards broad; the height of the wall iš required?

Anfwer 26,83+yards.