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
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
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
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
Thankyou guys so much
You're welcome.
To estimate the square root of a number that is not a perfect square without using a calculator, you can follow these steps:
Step 1: Find the two perfect square numbers that are closest to your given number. For example, if you want to estimate the square root of 20, you can find that the perfect squares closest to it are 16 (4^2) and 25 (5^2).
Step 2: Determine which perfect square your number is closer to. In this case, 20 is closer to 16 than it is to 25.
Step 3: Take the square root of the closest perfect square you identified. In our example, the square root of 16 is 4.
Step 4: Use this square root as an initial estimate for the square root of your given number.
Step 5: Refine your estimate by finding the difference between the initial estimate squared and the given number. In our example, 4^2 = 16, and the difference between 20 and 16 is 4.
Step 6: Divide this difference by twice the initial estimate. In our example, (20 - 16) / (2 * 4) = 1.
Step 7: Finally, subtract this quotient from the initial estimate. In our example, 4 - 1 = 3.
Therefore, the estimated square root of 20 is 3.
Remember, this method gives an approximate answer, and the actual value of the square root may be slightly different.