Question 1044700
start with sqrt(2 * sqrt(21) + 22) - sqrt(21) = 1


add sqrt(21) to both sides of the equation to get:


sqrt(2 * sqrt(21) + 22) = 1 + sqrt(21)


square both sides of this equation to get:


2 * sqrt(21) + 22 = 1 + 2 * sqrt(21) + 21


simplify to get 2 * sqrt(21) + 22 = 22 + 2 * sqrt(21)


this can also be written as:


2 * sqrt(21) + 22 = 2 * sqrt(21) + 22


the equation is true which proves that the original equation is true.


you can also use your calculator to confirm.


in your scientific calculator, enter:


sqrt(2 * sqrt(21) + 22) - sqrt(21)


you will see that the result is equal to 1.


if your calculator doesn't do square roots, you can alternatively enter the expression as:


(2 * 21^(1/2) + 22)^(1/2) - 21^(1/2)


the result will also be equal to 1.


note that (1 + sqrt(21))^2 is equal to:


(1 + sqrt(21) * (1 + sqrt(21) which is equal to:


1 * 1 + 1 * sqrt(21) + sqrt(21) * 1 + sqrt(21) * sqrt(21) which is equal to:


1 + sqrt(21) + sqrt(21) + 21 which is equal to:


1 + 2 * sqrt(21) + 21 which is equal to:


22 + sqrt(21).


this is through use of the distributive law of multiplication.