What is the squareroot of 85?

Answer 1

If you ask me, the best you can do with this is just give the approximation for this (9.2195444572928873100022742817628).

Normally, you can just factor out the smaller squares from the number and give the answer as a square-rooted factor multiplied by another prime factor. However, the only two factors in 85 are 17 and 5..... both of which are prime numbers, and can't be exactly reduced.

Good job to everyone else, just popping the numbers into a calculator and not even thinking about it. You guys are the smartest.... way to misinform.

Answer 2

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

Solution:
9 x 9 = 81 and 10 x 10 = 100, so square root of 85 lies between 9 and 10.

2. Divide - divide your number by one of those square roots.
(I would take “9” since 81 is closer to 85 than 100.)

Solution:
85/9 = 9.4444... (you can round off your answer)

3. Average - take the average of the result of step 2 and the root.

Solution:
(9.44 + 9)/2 = 9.2222...

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough.

Solution:
Repeat step 2: 85/9.2222 = 9.2169
Repeat step 3: (9.2222 + 9.2169)/2 = 9.2196

Try the answer --> 9.2196 x 9.2196 = 85.0010

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

I tried one more time and I came up with the same number.
85/9.2196 = 9.2195
(9.2196 + 9.2195)/2 = 9.2196
That means this is the end of it if you use 4 digits after decimal point.

But 9.2196 – 0.0001 (=9.2195)
9.2195 x 9.2195 = 84.9992
is actually closer.

Answer 3

9.21954457...
Squareroot of imperfect squares(like 85)leads to an irrational number.
You can round it off to 9.22 or 9.2195

Answer 4

The square root of 85 is 9.219544457 approx.

Answer 5

9.219544457

Answer 6

9.21954445729

Answer 7

9.22

Answer 8

9.219 exactly

Answer 9

9.2195444444444444444444444444444444444444444444444

Answer 10

9.21954445729288.....