SQUARE ROOTS OF FRACTIONS

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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