Square Root Number Lines Activity

Square Root Number Lines Activity 4) List the consecutive integers underneath the line that represent the square roots of each perfect square on You and your partner are receiving a strip of paper that is 45 your number line. inches long. With your strip horizontally in front of you, Ex: measure 5 in. from the left end and fold that section under the longer part of the strip. You should now have the 40 in. section in front of you.

Tasks:  Draw a number line towards the center of the strip. 5) What square root of a perfect square is each closest  Starting at the fold, measure and mark every two to? inches with a smaller mark in the middle to represent every 1 in. How do you know it is closest to that square root? 1) List all the perfect squares from 1 to 400. ______6) Now looking back at your number line, do you think 2) Plot each of the perfect squares as square roots on the any square roots should move? If so, which ones and number line on each 2 inch mark. why? If not, why do you think they don’t need to be Ex: moved? ______3) Place the following square roots in the proper place on ______your number line. 7) Using a calculator, find an approximate for each of the square roots. Round to the nearest thousandths. Name ______8) Did finding the approximate value of the square root 13) Unfold the 5 inches from the left side of your number change your mind about any of your placements on line and extend your number line to the left edge of the number line? Why? ______strip. Measure and mark every 2 inches. Then plot the ______second possibility we discovered for the and . ______14) Add either a “R” and “IR” to our new values on the number line. 9) On your number line, place an “R” next to the rational numbers and an “IR” next to the irrational numbers. 15) Label each square root on the top of the number line with a “I” if it’s an integer, “W” if it’s a whole number 10) What two consecutive integers does each square root and a “N” if it’s a natural number. fall between? 16) WITHOUT a calculator, estimate the following to the nearest tenth. ______11) Evaluate each expression. ______12) What do you notice for your answers in number 11? What does this mean about the and ?

Write a mathematical statement that would prove this is true.