What is the nearest integer to the square root of 85?
2 answers:
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:
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
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