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58.
a. 6/2 = 3, want 3 x 2= 6
b. √6/√2 = √3, want √3 x √2 = √6

59.
a. √10 / √2 = √(10/2) = √5
b. √5 / √5 = 1
c. √72 / √6 = √(72/6) = √12 = 2√3
d. √45 / √5 = √(45/5) = √9 = 3

60.
a. 4/2 ⋅ √(12/6) = 2√2
b. 10/5 ⋅ √(30/5) = 2√6
c. 20/5 ⋅ √(6/2) = 4√3
d. 12/4 ⋅ √(6/6) = 3 ⋅ 1 = 3
e. 12/6 ⋅ √(21/3) = 2√7
f. 30/12 ⋅ √(10/2) = 2½√5
g. 6/6 ⋅ √(42/7) = √6
h. 1/2 ⋅ √(5/5) = 1/2 ⋅ √1 = 1/2

61.
a. 12/3 ⋅ √(24/6) = 4 ⋅ √4 = 4 ⋅ 2 = 8
b. 12/3 ⋅ √(40/2) = 4 ⋅ √20 = 4 ⋅ √4 ⋅ √5 = 4 ⋅ 2 ⋅ √5 = 8√5
c. 5/2 ⋅ √(24/3) = 2½ ⋅ √8 = 2½ ⋅ √4 ⋅ √2 = 2½ ⋅ 2 ⋅ √2 = 5√2
d. 6/2 ⋅ √(12/3) = 3 ⋅ √4 = 3 ⋅ 2 = 6

62.
a. √(4/9) = √4 / √9 = 2/3
b. √(1/4) = √1 / √4 = 1/2
c. √(9/16) = √9 / √16 = 3/4
d. √(1/9) = √1 / √9 = 1/3
e. √(49/25) = √49 / √25 = 7/5 = 1 2/5
f. √(49/16) = √49 / √16 = 7/4 = 1 3/4
g. √(121/400) = √121 / √400 = 11/20
h. √(9/4) = √9 / √4 = 3/2 = 1 1/2

63.
a. 1/6√5
b. 2/7√7
c. 8/2√5 = 4√5
d. 18/12√6 = 1½√6

64.
a. √(21/4) = √21 / √4 = √21 / 2 = 1/2√21
b. √(10/9) = √10 / √9 = √10 / 3 = 1/3√10
c. √(81/16) = √81 / √16 = 9 / 4 = 2 1/4
d. √(24/9) = √24 / √9 = √4 ⋅ √6 / 3 = 2/3√6
e. √(50/16) = √50 / √16 = √25 ⋅ √2 / 4 = 5/4√2 = 1¼√2
f. √(78/25) = √78 / √25 = √78 / 5 = 1/5√78
g. √(60/49) = √60 / √49 = √4 ⋅ √15 / 7 = 2/7√15
h. √(169/64) = √169 / √64 = 13/8 = 1 5/8