Question

How do I prove if two numbers are reciprocals?

Estimate the value by the nearest tenth: [tex] \sqrt{221 }

What symbol makes everything a positive value?


If someone helps me answer this than I would greatly appreciate it.

Answer 1

1) a number multiplied by its reciprocal will always be 1, except for when the number is 0.

`n * (1)/(n) = (n)/(n) = 1, n \\eq 0`

So to verify if 2 numbers are reciprocals, just multiply them together and see if you get 1.


2) To estimate a sqrt, look at perfect squares.
10^2 = 100
11^2 = 121
12^2 = 144
13^2 = 169
14^2 = 196
15^2 = 225
16^2 = 256

221 is between 196 and 225, therefore sqrt(221) is between 14 and 15.
Much closer to 15

14.8^2 = 219
14.9^2 = 222

221 is closest to 222, so best estimate for sqrt(221) = 14.9


3)
Absolute value makes everything positive
|-3| = 3