Pick a two-digit number greater than 25. rewrite your two-digit number as a difference of two numbers. show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.

let's pick 35.

35 = 40 - 5

square both sides.

35^2 = (40 - 5)^2

now apply the square of a binomial to the right side, (x - y)^2 = x^2 - 2xy + y^2.

35^2 = (40 - 5)^2 =

= 40^2 - 2(40)(5) + 5^2

= 1600 - 400 + 25

= 1200 + 25

= 1225

35^2 = 1225

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: