Given S = 124, estimate the following
√124 using the sandwich method
Find the highest perfect square < 124
For n = 1, we have 12 = 1
For n = 2, we have 22 = 4
For n = 3, we have 32 = 9
For n = 4, we have 42 = 16
For n = 5, we have 52 = 25
For n = 6, we have 62 = 36
For n = 7, we have 72 = 49
For n = 8, we have 82 = 64
For n = 9, we have 92 = 81
For n = 10, we have 102 = 100
For n = 11, we have 112 = 121
For n = 12, we have 122 = 144
Since 122 = 144 > 124:
we use as our right endpoint.
Now, we find the low end number
(12 - 1)2 = 112 = 121
Therefore, √124 is between 11 and 12
11 < √124 < 12
What is the Answer?
11 < √124 < 12
How does the Estimate Square Roots Calculator work?
Free Estimate Square Roots Calculator - Estimates the square root of a number
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What 2 formulas are used for the Estimate Square Roots Calculator?
Take √n
Find n such that (n - 1)2 < n2 < (n + 1)2
Find n such that (n - 1)2 < n2 < (n + 1)2
What 5 concepts are covered in the Estimate Square Roots Calculator?
- estimate
- an approximate calculation or judgment of the value, number, quantity
- exponent
- The power to raise a number
- fraction
- how many parts of a certain size exist
a/b where a is the numerator and b is the denominator - power
- how many times to use the number in a multiplication
- square root
- a factor of a number that, when multiplied by itself, gives the original number
√x
