Question

Order the set of numbers from least to greatest: (4 points) square root 64, 8 and 1 over 7, 8.14 repeating 14, 15 over 2

Answer 1

Given numbers : $\sqrt{64} ,\ 8\frac{1}{7} , \ 8.141414... , \ \frac{15}{2}$

$\sqrt{64} = \sqrt{2*2*2*2*2*2}$

A pair of a number inside square root give a number out of square root.

We have three pairs of 2's are there.

Therefore,

$\sqrt{64} = \sqrt{2*2*2*2*2*2}=2*2*2=8$

$8 \frac{1}{7}=8.142857....$   ( Because 1/7 = 0.142857....)

8.14..... = 8.141414....

$\frac{15}{2}=7.5$                          (dividing 15 by 2 we get 7.5)

We can cleary see 7.5 is smallest number, second smaller is 8, and third one is 8.141414.... and finally fourth 8.142857.....

Subsituting original given numbers, we get

least to greatest :

$\frac{15}{2}, \ \sqrt{64} , \ 8.141414...,\ 8\frac{1}{7}$