Previously we have seen
32 = 9
indicates that
√9 = 3
Similarly,
(4/5)2 = 16/25
indicates that
√(16/25) = 4/5
From this, we observe
Example 1 :
Find √(4/9)
Solution :
√(4/9) = √4/√9
= √(2⋅2)/√(3⋅3)
= 2/3
Example 2 :
Find √(2 1/4)
Solution :
√(2 1/4) = √(9/4)
√(9/4) = √9/√4
= √(3⋅3)/√(2⋅2)
= 3/2
Example 3 :
Find √(25/9)
Solution :
√(25/9) = √25/√9
= √(5⋅5)/√(3⋅3)
= 5/3
Example 4 :
Find √(36/169)
Solution :
√(36/169) = √36/√169
= √(6⋅6)/√(13⋅1)
= 6/13
Example 5 :
Find √(160/5)
Solution :
√(160/5)
If it is possible, we can simplify and then find the square root.
= √32
= √(2⋅2⋅2⋅2⋅2)
= 2⋅2√2
√(160/5) = 4√2
Example 6 :
Find √(18/32)
Solution :
= √(18/32)
If it is possible, we can simplify and then find the square root.
= √9/16
= √9/√16
= √(3⋅3)/√(4⋅4)
√(18/32) = 3/4
Example 7 :
Find √(50/8)
Solution :
= √(50/8)
If it is possible, we can simplify and then find the square root.
= √25/4
= √25/√4
= √(5⋅5)/√(2⋅2)
√(50/8) = 5/2
Example 8 :
Find √(0.25/0.36)
Solution :
= √(0.25/0.36)
First change numerator and denominator as integer, and then take the square roots separately.
0.25 = 0.25 ⋅ (100/100) 0.25 = 25/100 |
0.36 = 0.36 ⋅ (100/100) 0.36 = 36/100 |
√(0.25/0.36) = √(25/100)/(36/100)
= √(25/36)
= √25/√36
= √(5⋅5)/√(6⋅6)
= 5/6
Example 9 :
Find √(0.81/0.4)
Solution :
= √(0.81/0.4)
First change numerator and denominator as integer, and then take the square roots separately.
0.81 = 0.81 ⋅ (100/100) 0.81 = 81/100 |
0.4 = 0.4 ⋅ (10/10) 0.4 = 4/10 |
√(0.81/0.4) = √(81/100)/(4/10)
= √(81/100)⋅(10/4)
= √(81/40)
= √81/√40
= √(9⋅9)/√(2⋅2⋅2⋅5)
= 9/2√10
Example 10 :
Find √(a3/b5)
Solution :
= √(a3/b5)
= √a3/√b5
= √(a⋅a⋅a)/√(b⋅b⋅b⋅b⋅b)
= a√a/(b⋅b)√b
= a√a/b2√b
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