Download Square Roots Review

14 Chapter Review
Vocabulary Help
Review Key Vocabulary
irrational number, p. 648
perfect cube, p. 634
real numbers, p. 648
theorem, p. 638
distance formula, p. 658
legs, p. 640
hypotenuse, p. 640
Pythagorean Theorem, p. 640
square root, p. 628
perfect square, p. 628
radical sign, p. 628
radicand, p. 628
cube root, p. 634
Review Examples and Exercises
14.1 Finding Square Roots
(pp. 626–631)
—
—
Find −√ 36 .
−√ 36 represents the
negative square root.
—
—
Because 62 = 36, −√ 36 = −√ 62 = −6.
Find the square root(s).
√
—
1. √ 1
—
9
25
3. ±√ 1.69
2. − —
Evaluate the expression.
—
4. 15 − 4√ 36
5.
14.2 Finding Cube Roots
√
—
√
—
54
6
2
3
— +—
—
6. 10( √ 81 − 12 )
(pp. 632–637)
—
Find
3
125
216
—.
()
5 3 125
Because — = —,
6
216
√
—
3
125
—=
216
Find the cube root.
3—
7. √ 729
√( )
—
5 3
5
= —.
6
6
3
√
—
—
8.
3
√−
—
64
343
—
9.
3
8
27
—
Evaluate the expression.
3—
10. √ 27 − 16
3—
11. 25 + 2√−64
3—
12. 3√−125 − 27
Chapter Review
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14.3 The Pythagorean Theorem
(pp. 638–643)
Find the length of the hypotenuse of the triangle.
a2 + b2 = c2
Write the Pythagorean Theorem.
72 + 242= c 2
Substitute.
49 + 576 = c 2
Evaluate powers.
625 = c 2
—
√ 625 = √ c 2
c
24 yd
Add.
—
Take positive square root of each side.
25 = c
Simplify.
The length of the hypotenuse is 25 yards.
7 yd
Find the missing length of the triangle.
14.
13.
c
12 in.
b
0.3 cm
35 in.
0.5 cm
14.4 Approximating Square Roots
(pp. 646–655)
—
a. Classify √ 19 .
—
The number √ 19 is irrational because 19 is not a perfect square.
—
b. Estimate √ 34 to the nearest integer.
Make a table of numbers whose squares are close to the radicand, 34.
Number
4
5
6
7
Square of Number
16
25
36
49
The table shows that 34 is between the perfect squares 25 and 36.
—
Because 34 is closer to 36 than to 25, √ 34 is closer to 6 than to 5.
16
25
4
5
34
36
49
6
7
—
So, √ 34 ≈ 6.
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Real Numbers and the Pythagorean Theorem
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Classify the real number.
—
15. 0.815
—
—
16. √ 101
17. √ 4
Estimate the square root to the nearest (a) integer and (b) tenth.
—
—
—
19. √ 90
20. √ 175
Write the decimal as a fraction.
—
—
22. 0.36
21. 0.8
—
23. −1.6
18. √ 14
14.5 Using the Pythagorean Theorem
(pp. 656 – 661)
a. Is the triangle formed by the rope and the tent a right triangle?
a2 + b2 = c2
?
642 + 482 = 802
?
4096 + 2304 = 6400
6400 = 6400
64 in.
80 in.
✓
It is a right triangle.
48 in.
b. Find the distance between (−3, 1) and (4, 7).
Let (x1, y1) = (−3, 1) and (x2, y2) = (4, 7).
——
d = √(x2 − x1)2 + ( y2 − y1)2
Write the distance formula.
——
= √ [4 − (−3)]2 + (7 − 1)2
Substitute.
—
= √ 72 + 62
Simplify.
—
= √ 49 + 36
Evaluate powers.
—
= √ 85
Add.
Tell whether the triangle is a right triangle.
24.
25.
Kerrtown
98 mi
61 ft
70
Snellville
16
11 ft
Big
g Lakee191
W
60 ft
in
104 mi
d
25
R
189
60
t
20
R
40 mi
59
Nicholton
Find the distance between the two points.
26. (−2, −5), (3, 5)
27. (−4, 7), (4, 0)
Chapter Review
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