Use a calculator and systematic trial to approximate each square root to 2 decimal places. SHow your work.
a) square root of 20=
B) Square root of 55=
c)square root of 115=
What would systematic trial mean and what do they mean by approximate each square root to 2 decimal places?? plz help!! thx:)
helpp plz
I don't know exactly what a systematic trial is here -- but it seems to me that you simply find the square root of these numbers and then round to the nearest hundredth.
Example:
square root of 20 = 4.472 = 4.47
exactly what Ms. Sue said square root of 20 is 4.472135 round that to 4.47. What perfect square is closest to 20. Like 4 squared is 16, 5 squared is 25. 16 IS CLOSER SO it will be more likely closer to 4 than 5 i dk if you are talking about this. Also think about your decimals, if you know it is not a perfect square think of a decimal which will multiply or square and give you a number which you will know when you add to four, the whole answer will be 20
To approximate each square root using a systematic trial, you can start by guessing some values and then refining them through a series of calculations until you reach the desired accuracy. The goal is to find a number that, when squared, comes close to the given value.
Approximating each square root to 2 decimal places means finding a value that is accurate up to two decimal places. For example, if the answer is 7.346, approximating it to 2 decimal places would be 7.35.
a) To approximate the square root of 20:
Start by guessing a number that could be close to the square root, like 4.
- Square the guess: 4^2 = 16
- Compare the squared value to 20:
- 16 is too low, so try a higher guess, for example, 5.
- Square the new guess: 5^2 = 25
- Compare the squared value to 20:
- 25 is too high, so the square root is somewhere between 4 and 5.
- Refine the guess by finding the midpoint between the two previous guesses:
- (4 + 5) / 2 = 4.5
- Square the new guess: 4.5^2 = 20.25
- Compare the squared value to 20:
- 20.25 is slightly higher, but very close to 20.
- The approximate square root of 20 to 2 decimal places is 4.5.
b) To approximate the square root of 55:
Start by guessing a number that could be close to the square root, like 7.
- Square the guess: 7^2 = 49
- Compare the squared value to 55:
- 49 is too low, so try a higher guess, for example, 8.
- Square the new guess: 8^2 = 64
- Compare the squared value to 55:
- 64 is too high, so the square root is somewhere between 7 and 8.
- Refine the guess by finding the midpoint between the two previous guesses:
- (7 + 8) / 2 = 7.5
- Square the new guess: 7.5^2 = 56.25
- Compare the squared value to 55:
- 56.25 is slightly higher, but very close to 55.
- The approximate square root of 55 to 2 decimal places is 7.5.
c) To approximate the square root of 115:
Start by guessing a number that could be close to the square root, like 10.
- Square the guess: 10^2 = 100
- Compare the squared value to 115:
- 100 is too low, so try a higher guess, for example, 11.
- Square the new guess: 11^2 = 121
- Compare the squared value to 115:
- 121 is too high, so the square root is somewhere between 10 and 11.
- Refine the guess by finding the midpoint between the two previous guesses:
- (10 + 11) / 2 = 10.5
- Square the new guess: 10.5^2 = 110.25
- Compare the squared value to 115:
- 110.25 is slightly lower, but very close to 115.
- The approximate square root of 115 to 2 decimal places is 10.5.
By following this systematic trial approach, you can approximate square roots to a desired level of accuracy.