Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality < √134 <

Here we have a problem with inequalities and square roots. We want to find two consecutive integers such that one is larger and another smaller than the given root.

We will find that these numbers are: 11 and 12

To find the numbers we need to find two consecutive numbers, x and (x + 1)

such that:

x^2 < 134

134 < (x + 1)^2

We can start with the lower bound, we need something that when squared is near 134, but lower, a good number is 11.

11*11 = 121 < 134

Then we can use x = 11

Then we will get (x + 1) = 11 + 1 = 12

And:

12*12 = 144 > 134.

Then we just found our two consecutive numbers:

11^2 < 134 < 12^2

Then if we apply the square root to the 3 sides, we get:

√(11^2) < √134 < √(12^2)

11 < √134 < 12

The two consecutive numbers are 11 and 12.

If you want to learn more, you can read:

link

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Step-by-step explanation:

We have been given an inequality . We are asked to find two consecutive integers to complete the following inequality.

We know that 121 is square of 11 and 144 is square of 12.

We also know that 11 and 12 are two consecutive integers. Since 11 is less than and 12 is greater than , so upon substituting 11 and 12 in our given inequality we will get,

.

entering that problem on the tube might get you an answer