Question

which number is to be subtracted from 10^2+2^2to get (10^-2)^2which number is to be separated from 10 square + 2 square to get 10 - 2 whole square ​

Answer 1

Answer:

103.9999

Step-by-step explanation:

Let $x$ be the number to be subtracted from 10^2+2^2 to get (10^-2)^2

ie.

$10^2+2^2-x=(10^{-2})^2$

To find this number we make x the subject of the formula

$10^2+2^2-x=(10^{-2})^2\\\\x=10^2+2^2-(10^{-2})^2$

But $(10^{-2})^2$ can be expressed as $(10^{-2})^2=(\frac{1}{10^2})^2=\frac{1}{10^4}$

Substituting this in the initial equation we get;

$x=10^2+2^2-(10^{-2})^2\\\\x=10^2+2^2-\frac{1}{10^4}\\ \\x=100+4-0.0001\\x=103.9999$

Therefore, the number is 103.9999