Question

What is square root of 114 approximated to the nearest tenth?

Answer 1

I'll medal!

Answer 2

sounds like you should get your calculator out and put in sqrt(114).

Answer 3

the hundredths digit will tell you to round or leave the tenth digit the same

Answer 4

okay, thanks

Answer 5

Do you want to tell me what you get after using the calculator and rounding to the nearest tenth?

Answer 6

sure

Answer 7

I can also show you how to approximate sqrt(114) without a calculator if you are interested

Answer 8

That would be cool, I suck at math

Answer 9

ok so you let's think about just the number inside the sqrt
the 114 that is
Let's think what two nearest perfect squares is 114 in between.
100 is a perfect square since 10*10=100
121 is a perfect square since 11*11=121
114 is certainly in between 100 and 121
that is we have the following inequality
\[100 <114<121\]

Answer 10

now the difference between 121 and 100 is 21
and the difference between 114 and 100 is 14
so 114 is 14/21 the distance between 100 and 121


ok let's keep that in mind

\[100 <114<121\]
take square root

\[10<\sqrt{114} <11\]
so we know that
\[\sqrt{114} \text{ is approximately } 10+\frac{14}{21}\]

Answer 11

you know because we already knew it was 10 something
since 10.something is between 10 and 11

Answer 12

so you can write 14/21 as a decimal then add the 10
then round to the nearest 10ths

Answer 13

that is an algebraic approach to approximate square roots
there are also other ways to approximate it like using calculus

Answer 14

thank you!

Answer 15

np