Question

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

Answer 1

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

Answer 2

so 14.5?

Answer 3

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

Answer 4

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

Answer 5

Thankyou guys so much

Answer 6

You're welcome.