What is sqrt((3-\sqrt{19))^2} ?

The solution to sqrt((3-\sqrt{19))^2} is sqrt(19)-3

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simplify sqrt((3-\sqrt{19))^2}

simplify

(3 - 19)^{2}

19 - 3

Solution steps

(3 - 19)^{2}

(3 - 19)^{2} = 28 - 619

= 28 - 619

= 19 - 619 + 9

= (19)^{2} - 619 + (9)^{2}

9 = 3

= (19)^{2} - 619 + 3^{2}

219 \cdot 3 = 619

= (19)^{2} - 219 \cdot 3 + 3^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(19)^{2} - 219 \cdot 3 + 3^{2} = (19 - 3)^{2}

= (19 - 3)^{2}

Apply radical rule:

(19 - 3)^{2} = 19 - 3

= 19 - 3

(x - (1 + i)) (x - (1 - i))

\frac{1}{8} \div 3

(6 a^{2} + 3 b) (3 b - 6 a^{2})

(X + 1)^{2}

(x + 6) + (x - 6)

What is sqrt((3-\sqrt{19))^2} ?
The solution to sqrt((3-\sqrt{19))^2} is sqrt(19)-3