Question

What is the nearest integer to the square root of 85?

Answer 1

Answer:

The answer is 9

Explanation:

Rounded to two decimal places, the Square root of 85 is 9.22. Rounded down to the nearest whole number, this is 9.

If you square 9, you get 9 x 9 = 81.

Answer 2

Answer:

9.2196

Explanation:

But you can get better and better approximations by: start with a number whose square is close to 85. (9 or 10.  

9

2

is closer, so start there.

Now divide 85 by  

9

to get  

9.4444

(to 4 places)

Average the two numbers  

9

and  

9.4444

9

+

9.4444

2

=

9.2222

Repeat:

85

÷

9.2222

=

9.2169

(rounded to 4 places)

Average:  

9.2222

+

9.2169

2

=

9.2196

Repeat:

85

÷

9.2196

=

9.2195

(rounded to 4 places)

Average:  

9.2196

+

9.2195

2

=

9.2196But you can get better and better approximations by: start with a number whose square is close to 85. (9 or 10.  

9

2

is closer, so start there.

Now divide 85 by  

9

to get  

9.4444

(to 4 places)

Average the two numbers  

9

and  

9.4444

9

+

9.4444

2

=

9.2222

Repeat:

85

÷

9.2222

=

9.2169

(rounded to 4 places)

Average:  

9.2222

+

9.2169

2

=

9.2196

Repeat:

85

÷

9.2196

=

9.2195

(rounded to 4 places)

Average:  

9.2196

+

9.2195

2

=

9.2196