Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 21, 2023

Find the two integers that bound the square root of 115.

STEP 1

Assumptions1. We are looking for two consecutive integers between which the square root of115 lies.

STEP 2

To find out between which two integers the square root of115 lies, we need to find the square roots of the integers around115 until we find two consecutive integers where the square root of115 lies in between.

STEP 3

We start by finding the square root of the integer below115. Let's start with10 because $10^2 =100$ which is the closest perfect square less than115.
$\sqrt{10^2} =10$

STEP 4

Next, we find the square root of the integer above115. We know that $11^2 =121$ which is the closest perfect square greater than115.
$\sqrt{11^2} =11$

STEP 5

Now, we know that the square root of115 lies between10 and11 because $10^2 <115 <11^2$ .
So, the square root of115 lies between10 and11.

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