If you know the square root of the numbers just above and below your number, you can make a good estimate.
For instance, what would you estimate the square root of 200 to be?
14 is the square root of 196
15 is the square root of 225
please some help me I'm stuck on this question describe how to estimate the square root of a number that is not a perfect square without a calculator please make it as simple as possible 7th grade math connections
6 answers
so 14.5?
That's close. I'd estimate it to be closer to 14.2.
https://www.google.com/search?source=hp&ei=MAJ1WvrSBoivjwTi9p64AQ&q=square+root+200&oq=square+root+200&gs_l=psy-ab.3..0l2j0i22i30k1j0i22i10i30k1j0i22i30k1l6.4255.11853.0.15400.15.12.0.3.3.0.83.437.12.12.0..3..0...1c.1.64.psy-ab..0.15.467...0i131k1j0i10k1.0.XfiFdczwwJU
https://www.google.com/search?source=hp&ei=MAJ1WvrSBoivjwTi9p64AQ&q=square+root+200&oq=square+root+200&gs_l=psy-ab.3..0l2j0i22i30k1j0i22i10i30k1j0i22i30k1l6.4255.11853.0.15400.15.12.0.3.3.0.83.437.12.12.0..3..0...1c.1.64.psy-ab..0.15.467...0i131k1j0i10k1.0.XfiFdczwwJU
what would you estimate the square root of 200 to be?
guess poorly at first
x = 13 so x^2 = 169
(x+a)^2 = x^2 + 2 a x + a^2 = 200
assuming a is much smaller than x this is about
x^2 + 2 a x = 200
169 + 2a(13) = 200
26 a = 31 or around 25 a = 30 or a =6/5
so my first guess is
x = 13 + 1.2 = 14.2
now do it all again starting with x = 14.2
guess poorly at first
x = 13 so x^2 = 169
(x+a)^2 = x^2 + 2 a x + a^2 = 200
assuming a is much smaller than x this is about
x^2 + 2 a x = 200
169 + 2a(13) = 200
26 a = 31 or around 25 a = 30 or a =6/5
so my first guess is
x = 13 + 1.2 = 14.2
now do it all again starting with x = 14.2
Thankyou guys so much
You're welcome.