Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

4. Find the square root of 30,625.

175

30625

1

27 206
189
345 1725

In case the number whose root is to be found consists of more than two periods, repeat the process used in finding the second root figure.

[blocks in formation]

In separating a decimal into periods, begin at the decimal point and point off to the right. If the last period is not full, annex a cipher.

[merged small][ocr errors][merged small]

In separating a whole number and a decimal into periods, begin at the decimal point and point off the whole number to the left and the decimal to the right.

[blocks in formation]

1. Find the square root of: (1) 436.81; (2) .2.

[blocks in formation]

Since the trial divisor, 4, is not contained in 3, place a 0 in the root, annex a 0 to the trial divisor, 4, and bring down the next period.

(2)

.4 4 7+

.200000

16

84 400
336
887 6400

6209
191

Annex as many O's as may be necessary.

2. Find the square root of: (1) 11‡; (2) ‡.

When both numerator and denominator are perfect squares, extract the root of each term. First change the fraction to a decimal.

(1) √t = 号

(2) √‡ = √.142857

[ocr errors]

.377+

3. Tell which of these numbers are perfect squares:

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

Find the square roots to the third decimal place:

30.

131

1936 2401

31. 4988

4096

35. 721

[blocks in formation]

PROBLEMS

1. What is the length of one side of a square wood lot containing 15 acres?

2. What is the distance around a square field containing 10 acres?

3. Mr. Morrison's house is 36 feet square, and stands in a square lot containing 9025 square feet. Find the area covered by the house. Find the length of the lot.

4. How many feet of picture molding will be required for a square room whose ceiling covers 256 square feet?

5. The entire outside surface of a cubical block is 1350 square inches. Find the dimensions of the block.

6. Find the dimensions of a square plate-glass window whose surface area is 56.25 square feet.

7. Mr. Draper's potato field is 147 feet long and 48 feet wide; his cornfield is a square of equal area. Find the dimensions of the cornfield.

8. A party of school children went on an excursion, paying $12.25 for car fares. Each child's share of the expense was as many cents as there were children in the party. How much did each pay?

THE RIGHT-ANGLED TRIANGLE

In a right-angled triangle the side opposite the right angle is the hypotenuse. Thus, the line AC is the hypotenuse of the right-angled triangle ABC on page 402.

ABC is a right-angled triangle whose altitude, base, and hypotenuse are 3 inches, 4 inches, and 5 inches, respectively. How many square inches in the square on the hypotenuse? In the square on the altitude? In the square on

the base? How does the square on the hypotenuse compare with the sum of the squares on the altitude and base?

[blocks in formation]

In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Letting h represent the hypotenuse, a the altitude, and b the base, this fact may be stated thus: h2= a2 + b2.

The hypotenuse of a right-angled triangle is equal to the square root of the sum of the squares on the other two sides.

This may be stated thus: h=Va2 + b2.

1. The altitude of a right-angled triangle is 6 feet and the base 8 feet. Find the hypotenuse.

[blocks in formation]

Solve.

h = √62 +82 = √100=10

2. Tell what this means: a = Vh2b2.

3. If the hypotenuse is 10 feet and the base 8 feet, what is the altitude?

4. What is the base of a right-angled triangle whose hypotenuse is 10 feet and whose altitude is 6 feet? Write formula and show solution.

Find the hypotenuse of the following right-angled triangles whose dimensions are given in feet:

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
« ΠροηγούμενηΣυνέχεια »