Groups

# Maths question whats the square root of 99 how do i work it out?? please be kind

Just looking at some maths videos on youtube, and i was messing around with some maths doodling on some paper and what not :), and i was having a little trouble working this one out please if u can help me i would i appreciate it thanx!

SQRT(99) is an irrational, approximately equal to 9.95. [I bet you already
knew that it was just a little less than 10] Here's how I came up with
9.95 without using a calculator:
Since 10^2 = 100, SQRT(99) must be 10-d where d is much smaller than 1.
A little algebra:
(10-d)*(10-d)=99
100-20*d+d*d =99
1-20*d+d*d = 0
1-20*d = -d*d, but d and for a good approximation, we can assume it's 0:
1-20*d ~= 0
ergo d = 1/20 = 0.05
The actual value of SQRT(99) is 9.94987, so our approximation is pretty
good.

9.9498743710662

Turn calculator on

Type "99"

Press square root button

Done

trial & error says its somewhere between 9.94 & 9.95.

Original Poster

skusey;7842395

Answer:SQRT(99) is an irrational, approximately equal to 9.95. [I bet you … Answer:SQRT(99) is an irrational, approximately equal to 9.95. [I bet you alreadyknew that it was just a little less than 10] Here's how I came up with9.95 without using a calculator:Since 10^2 = 100, SQRT(99) must be 10-d where d is much smaller than 1.A little algebra: (10-d)*(10-d)=99 100-20*d+d*d =99 1-20*d+d*d = 0 1-20*d = -d*d, but d and for a good approximation, we can assume it's 0: 1-20*d ~= 0 ergo d = 1/20 = 0.05The actual value of SQRT(99) is 9.94987, so our approximation is prettygood.

:w00t:

Banned

ChrisUK;7842409

Turn calculator onType "99"Press square root buttonDone

job done!

dav1d_uk;7842549

job done!

+1 ... lol

Original Poster

arcangel111;7842604

+1 ... lol

- 1 :roll:;-) maths is fun when your not cheating, with a calculator or looking up the answers, on google and then pasting the answers here:-D

skusey;7842395

Answer:SQRT(99) is an irrational, approximately equal to 9.95. [I bet you … Answer:SQRT(99) is an irrational, approximately equal to 9.95. [I bet you alreadyknew that it was just a little less than 10] Here's how I came up with9.95 without using a calculator:Since 10^2 = 100, SQRT(99) must be 10-d where d is much smaller than 1.A little algebra: (10-d)*(10-d)=99 100-20*d+d*d =99 1-20*d+d*d = 0 1-20*d = -d*d, but d and for a good approximation, we can assume it's 0: 1-20*d ~= 0 ergo d = 1/20 = 0.05The actual value of SQRT(99) is 9.94987, so our approximation is prettygood.

Lmao!

skusey;7842395

Answer:SQRT(99) is an irrational, approximately equal to 9.95. [I bet you … Answer:SQRT(99) is an irrational, approximately equal to 9.95. [I bet you alreadyknew that it was just a little less than 10] Here's how I came up with9.95 without using a calculator:Since 10^2 = 100, SQRT(99) must be 10-d where d is much smaller than 1.A little algebra: (10-d)*(10-d)=99 100-20*d+d*d =99 1-20*d+d*d = 0 1-20*d = -d*d, but d and for a good approximation, we can assume it's 0: 1-20*d ~= 0 ergo d = 1/20 = 0.05The actual value of SQRT(99) is 9.94987, so our approximation is prettygood.

choc1969;7843142

LOL.. caught out....well spotted....:thumbsup:

Iteration :

We know that 10x10=100 and 9x9=81 so the square root of 99 is definitely between 9 and 10. Hopefully it is apparent that the answer is likely to be closer to 10 than it is 9. In order to find out if the answer is closer to 10 or 9 you would calculate 9.5x9.5 (=90.25) and see if you need a number greater than or less than 9.5. Hopefully you'd be able to see that calculating 9.9x9.9 (=98.01) would be a good idea. You would then need to calculate 9.95x9.95 (=99.025) to see if you need a number greater or less than 99.5. You would keep repeating this method of calculation (iterating) until you reach the desired number of decimal places.

I hope that explains it :-)

10 * 10 = 100 (too big)
9 * 9 = 81 (too small)
9.5 * 9.5 = 90.25 (too small)
9.9 * 9.9 = 98.01 (too small)
9.95 * 9.95 = 99.025 (too big)
9.94 * 9.94 = 98.8036 (too small)
9.945 * 9.945 = 98.903025 (too small)
9.949 * 9.949 = 98.982601 (too small)
9.9495 * 9.495 = 98.9925503 (too small)

and so on.....

Banned

choc1969;7843142