Answer:
[tex]5\sqrt{3}[/tex] OR [tex]8.69[/tex]
Step-by-step explanation:
Let's first simplify [tex]\sqrt{75}[/tex].
5 and 15 multiply to get 75. 5 and 3 multiply to get 15. Since we have a pair of fives and a three leftover, we can write [tex]\sqrt{75}[/tex] as:
[tex]5\sqrt{3}[/tex]
Now, let's find the answer in decimal form. We know that:
[tex]8^2=64[/tex] and [tex]9^2=81[/tex]
With that information, we know that the answer has to be between 8 and 9.
Divide 75 by 8: [tex]\frac{75}{8}=9.375[/tex]
Take the average of that answer and 8: [tex]\frac{9.375+8}{2}=\frac{17.375}{2}=8.6875[/tex]
This answer we got is extremely close to the exact answer of [tex]\sqrt{75}[/tex], which is [tex]8.66025403...[/tex]. Since we are estimating, the answer above will do just fine.
