untitled

4.3nth root

We notice,

2

2

1

2

1

2

1

5 5 5 ̧

¹

·

̈

©

§

u

Again, 5 2 5

21

2

1

2

1

2

1

2

1

5 5 5

 u

u

5 5.

2

2

1

? ̧

¹

·

̈

©

§

Square (power 2) of^25

1

5 and square root (second root) of 5 =^2

1

5

2

1

5 is written as 5 in terms of the sign of square root.

Again, we notice

3

3

1

3

1

3

1

3

1

(^5555) ̧ ̧
¹
·
̈
̈
©
§
u u
Again, 5 3 5
31
3
1
3
1
3
1
3
1
3
1
3
1
5 5 u 5 5
 u
u
5 5.
3
3
1
? ̧ ̧
¹
·
̈ ̈
©
§
Cube (power 3) of^3
1
5 = 5 and cube root (third root) of 5 =^3
1
5.
3
1
5 is written as^35 in terms of the sign^3 of cube root.
In the case of nth root,
.
.......
1
1 1 1 1
n
n
n n n n
a
a a a a
̧ ̧
¹
·
̈ ̈
©
§
u u u u
Again,an an an an
1 1 1 1
u u u.......u
a a
a
nn
nnn n
u
 
1
(^111) .......... 1
.
1
a a
n
n
̧
̧
¹
·
̈
̈
©
§
?
nth power of an
1
a and nth root of a an
1
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