Question

How do I solve this? I need to learn how to do it but I don't understand how to do it...so yea..

Answer 1

Use a calc.

Answer 2

Since you dont have to write the original value.
you have to write in decimals.

Otherwise what we do is, factor the term inside the radical.

Answer 3

\[\sqrt{756} = \sqrt{36*21}=\sqrt{36}\sqrt{21}=6\sqrt{21}\]

Answer 4

if you don't have a calculator and want to approximate it anyways, you can try converting 21 into a fraction with a square as a denominator. sqrt(21) = sqrt(84/4) which is "close" to sqrt(81/4), which gives you 9/2. so sqrt(21) is slightly more than 4.5

Answer 5

I don't really understand...

Answer 6

Yeah, it may a bit too complicated I guess. Stick with getting a calculator for now, it's much simpler. The fraction thing is something you'd do if you were stuck in a desert with an airplane missing a wing and you need to afix it anyways and you absolutely had to calculate sqrt(21) to escape! But I digress.

Did you at least get what agreene was explaining?

Answer 7

since we dont know what level of math your capable of understaning, your revelation of confusion doesnt really help us to focus on what it is that you are actually confused about.

Answer 8

There is an approximation that comes from a taylor series expansion.
\[ \sqrt{1+\epsilon} \approx 1+\frac{\epsilon}{2}\]

we can use this tidbit by picking a nearby square. e.g. 27*27= 729
that means we can write 756 as 729 + 27

\[ \sqrt{27^2+27} = 27\sqrt{1+\frac{1}{27}}\]
now use the approximation
\[ 27\cdot(1+\frac{1}{54}) =27\cdot 1.0185= 27.5 \]
to the nearest tenth

27.5^2 = 756.25 which is close

Answer 9

I should point out that this approximation works well only for |epsilon| << 1

Answer 10

see. clear as abell ;)

Answer 11

Ohh ok! Thank you guys!