Give a decimal estimate to two places
(hundredths) for this irrational number. Be sure
to get a decimal estimate for the square root

(using a calculator) before doing anything else.

To estimate , you can use a calculator, which gives you approximately 3.74. Adding this to 3, you get:

So, the decimal estimate for to two decimal places is approximately 6.74.

But did you know? The square root of 14 isn’t just a quirky number; it’s actually the distance from the origin to the point in a 2D grid! This concept of distance can be imagined as the hypotenuse of a right triangle, with the other sides being √(12.14) and √(1). Geometry in action!

When estimating or calculating square roots, many people mistakenly think every square root yields a whole number, which is not the case with irrational numbers like 14. Always remember to use a calculator or estimation methods, like the averaging technique, to clarify your understanding!