Question

Using the ratio of perfect squares method, what is square root of 53 rounded to the nearest hundredth?

Do not use your calculator to answer this question. Use the ratio of perfect squares method.
Hi! I don't understand how to do ratio of squares method, please help!

Answer 1

@iGreen :)

Answer 2

to be honest i've never heard of it...
the 2 perfect squares either side of 53 are 49 and 64 so i expect they must get involved in it.

Answer 3

I guess its not a very common method :(

Answer 4

I will give an example of the ratio of perfect squares to find the square root of 26:
5^2=25<26
6^2=36>26
so sqrt(26) is between 5 and 6.
We interpolate for the square-root as follows:
square root of 26 approximately equals:
5 + (26-25)/(36-25)=5 + 1/11= 5.090909...=5.09
check: exact value of sqrt(26)=5.099... a "little" off.

If you'd like a more accurate method, let me know.

Answer 5

Do you always divide by 11? Or do you just add 5 and 6 (or whatever the numbers turn out to be) and divide by that? @mathmate

Answer 6

11=36-25, so it is the difference of the squares bracketing the required square-root.
Note: 26-25=1, 36-25=11

Answer 7

I learnt something today! ty

Answer 8

Thanks a lot friend, I understand :D Medal and fan coming your way. @mathmate