Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[graphic][merged small][merged small][merged small][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][ocr errors]

OF THE SQUARE ROOT. Q. What is a Square ? A. Any number multiplied by itself produces a square, Q. What is the Extraction of the Square Root?

A. If a square be given to find one side, it is called the extraction of the Square Root.

Q. How is the given Square to be prepared for extraction?

A. By pointing off at every two figures, from the units place, both ways for a resolvend.

Q. What is a Surd ?.

A. It is an imperfect Square, or such a number whose Square Root can never be exactly found.

EXAMPLES. 1 What is the Square of 17.1? Answ. 292. 41 2 What is the Square of.09? Answ. .0081 3 What is the Square of .0094?. Answ..00008336 4 What is the Square Root

Answ. 68.649 + of 4712.81261? 5 What is the Square Root

Answ. 98.553 + of 9712.718651? 6 What is the Square Root

Answ. 1.78106+ of 3,1721812 ? 7 What is the Square Root ,

Answ. 1,1822+ of 1.3976121? 8 What is the Square Root

Answ. 27.6007+ of 761.801216? 9 What is the Square Root

Answ..02759+ of 0007612816? 10 What is the Square Root

Answ. 2.000016+ of 4,000067121?

11 There is an army consisting of a certain number of men, who are placed rank and file, that is, in the form of a Square, each side having 47.2 men; I demand how

many men the whole

square

contains ? Ans. 222784 men, 12 The floor of a certain great room is tdade exactly square, each side of which contains 75 feet? I demand how many Square feet are contained therein? Ans. 5625 feet.

13. Suppose 12 544 Soldiers are to be put into rank and file, in the form of an equal square ; I demand how many soldiers will be in the front,and how many deep? Ans 112.

14 A certain square pavement contains 197 136 square stones ail of the same size; I demand how many are contained in one of its sides ? Ans. 414..

15 The wall of a town is 17 feet high, which is sur. rounded by a moat, of 20 feet in breadth; I demand the length of a ladder which shall reach from tle outside of the moat to the top of the wall i Answer 26.2+feet. OF THE SQUARE ROOT OF A VULGAR FRAC

TION.

Q. How is the Square Root of a Vulgar Fraction extracted ? A. Reduce the Fraction to its lowest terms.

2 Extract the Square Root of the Numerator for a new Numerator, and the Square Root of the Denominator for a new Denominator..

3 If the fraction be a Surd, reduce it to a Decimal, and then extract the Square Root from it.

4 The Decimal Fractions must consist of an eyen num. her of places, as two, four, &c.

EXAMPLES.

1 What is the Square-Root of ? Answer {.
2 What is the Square-Root of 466? Answer
3 Vhat is the Square-Root of joil Answers

Surds.
4 What is the Square-Root of 3197? Answer .71528+
5 What is the square-Root of ? Answer .87447 +

6. What is the Square-Root of ? Answer.72414+ OF THE SQUARE-ROOT OF A MIXT NUMBER.

Q. How is the Square-Root of a mixt number extracted?

A. ! Reduce the Fractional part of the mixt number to its lowest term.

2 Reduce the mixt vumber to an improper fraction.

3 Extract the Roots of the Numerator and Denominator, for a new Numerator and Denominator.

4 If the mixt number given be a Surd, reduce the fractional part to a Decimal, and annex it to the whole number, and extract the Square-Root from the whole.

EXAMPLES." 1 What is the Square-Root of 373 ? Answer 64 2 What is the Square-Root of 1728? Answer 5* 3 What is the Square-Root of 532? Answer 2.

SURDS. 4 What is the Square-Root of 7614 ? Answer 8.7649 + 5 What is the Square-Bdot of 778? Answer 2.79617

OF THE CUBE-ROOT:

Q. WHAT is a Cube?

3. Any Number multiplied by its Square, produces a Cube.

Q. What is the extraction of the Cube-Root ?

A. If a Cube be given to find out a Number, which, be: ing multiplied into its Square, produceth the number given ; this is called the extraction of the Cube-Root

Q. How is the given Cube to be prepared for Extraction ?

Ā. Bv pointing off at every three Figures, both ways, from the unit's place, for a resolvend.

Q. What is a Surd ?

A. It is an imperfect Cube, or such a number, whose Cube-Root can never be exactly found.

Q. What is the rule for extracting the Cube-Root of a Number:

A. This: the first figure sought is the 'Root of the greatest Cube contained in the first member, and it is called a; then 3aa3+ a is the Divisor, which finds a new figure called e; then 3ade +een toeee is the Subtrahend or Number to be subducted; which operation is to be continued to every resolvend.

Note. This rule being somewhat dark, I shall, by way of illustration, subjoin the operation at large for extracting the Cube-Root of any number.

What is the Cube-Root of 444194.947 ? (1) Let the given Number be pointed as before directed;

thus: 444194.947 (2) The first member, which contains the greatest Cube, is 444; and the nearest Root, whose Cube is not greater than is, is 7, which set .

thus : 444194.94767 (3) The Cube of 7 is 343, which set down and subtract, annexing the next three figures, or member, viz. 194 for a resolvend;

thus: 444194.94767

343

101194 Resolvend. (4) The number 7, in the Root is called v; then by the Rule 3aa+3a is the Divisor; thus,

1

[blocks in formation]

Divisor 1491=jaat 3a (5)

The next figure in the Root, viz. 6 (found by common Division) is called e; then by the rule 3aae73eea +eee is the Subtrahend, or Number to be subducted; thus, 147=3aa

63 6=e

eee viz. 6=216 6=e

[blocks in formation]

5213.947 Resolvend. (6) When the next number is brought down, viz. 947 as before, both figures in the Root, viz. 76 must be called a;

then to find a Divisor to this last Resolvend, say, as before, 3aa+3a; thus, 765a

76 76=a

3= 456

228=3a 444194.947(76 532

343

5776=aa

1491(101194 Resolvend

95976 Subtrahend N

« ΠροηγούμενηΣυνέχεια »