ROOTS OF INTEGERS
For every two same numbers multiplied inside the square root, one number can be taken out of the square root.
For every three same numbers multiplied inside the cube root, one number can be taken out of the cube root. The same procedure can be followed for fourth root and more.
Example 1 :
Evaluate : √4.
Solution :
√4 = √(2 x 2)
= 9
Example 2 :
Evaluate : √16.
Solution :
√16 = √(4 x 4)
= 4
Example 3 :
Evaluate : √64.
Solution :
√64 = √(8 x 8)
= 8
Example 4 :
Evaluate : √144.
Solution :
√144 = √(12 x 12)
= 12
Example 5 :
Evaluate : 3√27.
Solution :
3√27 = 3√(3 x 3 x 3)
= 3
Example 6 :
Evaluate : 3√-8.
Solution :
3√-8 = 3√[(-2)(-2)(-2)]
= -2
Example 7 :
Evaluate : 3√512.
Solution :
3√512 = 3√(8 x 8 x 8)
= 8
Example 8 :
Evaluate : 3√-8000.
Solution :
3√-8000 = 3√[(-20)(-20)(-20)]
= -20
Example 9 :
Evaluate : 4√64.
Solution :
4√16 = 4√(2 x 2 x 2 x 2)
= 2
Example 10 :
Evaluate : 4√81.
Solution :
4√81 = 4√(3 x 3 x 3 x 3)
= 3
Example 11 :
Evaluate : 5√32.
Solution :
5√32 = 5√(2 x 2 x 2 x 2 x 2)
= 2
Example 12 :
Evaluate : 5√243.
Solution :
5√243 = 5√(3 x 3 x 3 x 3 x 3)
= 3
Example 13 :
Evaluate : √8.
Solution :
√8 = √(2 x 2 x 2)
= 2√2
Example 14 :
Evaluate : √45.
Solution :
√45 = √(3 x 3 x 5)
= 3√5
Example 15 :
Evaluate : 3√54.
Solution :
3√54 = 3√(3 x 3 x 3 x 2)
= 33√2
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