Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches. √3 2√3 √5 (a) Without using your calculator, approximate the decimal equivalent of each number to the

Question

nearest tenth. (b) Order the ribbon sizes from least to greatest

Answer 1

√3:
3 is not a perfect square, but the nearest perfect squares are 1 and 4.
Thus √3 lies somewhere between √1 and √4.

Picture the numbers 1, 3 and 4 on a number line.
It takes 2 jumps to get from 1 to 3.
It takes 3 jumps to get from 1 to 4.
That means 3 is 2/3 of the way between 1 and 4.

So, we could estimate √3 to be 2/3 of the way between √1 and √4, or in other words, 2/3 of the way between 1 and 2.

1+ 2/3 = 1 2/3
To get this number to the nearest tenth, you would need to manually divide 2 by 3...or you might already know that 2/3 is 0.66666......

1 + 0.66666...... = 1.66666..... ~ 1.7 ( nearest tenth)

You can follow similar reasoning to find √5.