Given S = 136, estimate the following

√136 using the sandwich method

Find the highest perfect square < 136

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 > 136:
we use as our right endpoint.

Now, we find the low end number
(12 - 1)2 = 112 = 121

Therefore, √136 is between 11 and 12

11 < √136 < 12

What is the Answer?

11 < √136 < 12

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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

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What 5 concepts are covered in the Estimate Square Roots Calculator?

estimatean approximate calculation or judgment of the value, number, quantityexponentThe power to raise a numberfractionhow many parts of a certain size exist
a/b where a is the numerator and b is the denominatorpowerhow many times to use the number in a multiplicationsquare roota factor of a number that, when multiplied by itself, gives the original number
√x

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