Approximate square root of, 59, end square root
59
59
by following the steps below.
square root of, 59, end square root
59
59
must lie between the whole numbers
and
Answer
Attempt 1 out of 2
You must answer all questions above in order to submit.
The square root of 59 lies between the whole numbers 7 and 8.
Approximate square root of, 59, end square root
59
59
by following the steps below.
square root of, 59, end square root
59
59
must lie between the whole numbers
7
7 and
8
8 because 7, squared, equals, start box, 49, end box
7
2
=
49
7
2
=
49
and 8, squared, equals, start box, 64, end box
8
2
=
64
8
2
=
64
, and 59 lies between these values.
Drag square root of, 59, end square root
59
59
based on your estimate above:
Real
√59
__
_
To one decimal place, square root of, 59, end square root
59
59
must lie between
and
because 7, squared, equals, start box, 49, end box
7
2
=
49
7
2
=
49
and 8, squared, equals, start box, 64, end box
8
2
=
64
8
2
=
64
, and 59 lies between these values.
To one decimal place, the square root of 59 lies between 7.0 and 8.0.
Between which two consecutive whole numbers does square root of, 11, end square root
11
11
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 11, end square root
11
11
to an approximately correct location on the number line.
Real
√11
__
_
Answer
Attempt 2 out of 2
Since square root of, empty space, end square root
2
2
equals
=
=
and square root of, empty space, end square root
2
2
equals
=
=
it is known that square root of, 11, end square root
11
11
is between
and
.
Since the square root of 4 equals 2 and the square root of 9 equals 3, it is known that the square root of 11 lies between 2 and 3.
To find the approximate square root of 59, we can use the method of estimation.
Step 1: Start by guessing a number that could be the square root of 59. Let's guess 7.
Step 2: Divide 59 by the guess 7 to get 8.43 (rounded to 2 decimal places).
Step 3: Take the average of the guess and the result from step 2: (7 + 8.43) / 2 = 7.715 (rounded to 3 decimal places).
Step 4: Repeat steps 2 and 3 with the new guess.
- Divide 59 by 7.715 to get 7.649 (rounded to 3 decimal places).
- Take the average of the guess and the result from step 4: (7.715 + 7.649) / 2 = 7.682 (rounded to 3 decimal places).
Step 5: Repeat steps 2 and 3 with the new guess.
- Divide 59 by 7.682 to get 7.685 (rounded to 3 decimal places).
- Take the average of the guess and the result from step 5: (7.682 + 7.685) / 2 = 7.684 (rounded to 3 decimal places).
Continue this process until you reach a desired level of accuracy.
Based on this method, the approximate square root of 59 is 7.684 (rounded to 3 decimal places).
To approximate the square root of 59, we can follow these steps:
Step 1: Find the two whole numbers between which the square root of 59 lies. To do this, we need to look for perfect squares that are closest to 59. The perfect squares near 59 are:
7^2 = 49
8^2 = 64
So, the square root of 59 must lie between 7 and 8 since 59 is closer to 64 than 49.
Step 2: Take the average of the two whole numbers. In this case, the average of 7 and 8 is (7 + 8) / 2 = 7.5.
Therefore, the approximate square root of 59 is 7.5.
Keep in mind that this is an approximation since the actual square root of 59 is a non-recurring decimal.