The square root of 105 would lie between which two consecutive integers?
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Greetings!
To start this problem, let's first assign a variable for the missing, consecutive odd numbers. Since they are consecutive and odd, we add two.
<u>Proof:</u> <em>3-1=2, 5-3=2</em>
The first, consecutive, odd number:
The second, consecutive, odd number:
The third, consecutive, odd number:
The fourth, consecutive, odd number:
The sum of the values are equal to 3 times the sum of the first two numbers, of which this is equal to 35 less than the fourth number. Let's create an equation to simplify this:
Complete the operations inside the parenthesis:
Distribute the parenthesis (utilizing the distributive property)
Simplify both sides:
Add -6 and -x to both sides of the equation:
Divide both sides of the equation by 5:
If is equal to -7:
The four numbers are:
I hope this helps!
-Benjamin