Question

what is the square root of 90 by estimation process explain​

Answer 1

√√

9090

==

33

√√

1010

≈≈

10396811039681

109592

≈

9.48683298051

Explanation:

√

90

=

√

3

2

⋅

10

=

3

√

10

is an irrational number somewhere between

√

81

=

9

and

√

100

=

10

.

In fact, since

90

=

9

⋅

10

is of the form

n

(

n

+

1

)

it has a regular continued fraction expansion of the form

[

n

;

¯¯¯¯¯¯¯¯

2

,

2

n

]

:

√

90

=

[

9

;

¯¯¯¯¯¯¯¯

2

,

18

]

=

9

+

1

2

+

1

18

+

1

2

+

1

18

+

1

2

+

1

18

+

...