What is sqrt((2-\sqrt{5))^2} ?

The solution to sqrt((2-\sqrt{5))^2} is sqrt(5)-2

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simplify sqrt((2-\sqrt{5))^2}

simplify

(2 - 5)^{2}

5 - 2

Solution steps

(2 - 5)^{2}

(2 - 5)^{2} = 9 - 45

= 9 - 45

= 5 - 45 + 4

= (5)^{2} - 45 + (4)^{2}

4 = 2

= (5)^{2} - 45 + 2^{2}

25 \cdot 2 = 45

= (5)^{2} - 25 \cdot 2 + 2^{2}

Apply Perfect Square Formula:

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

(5)^{2} - 25 \cdot 2 + 2^{2} = (5 - 2)^{2}

= (5 - 2)^{2}

Apply radical rule:

(5 - 2)^{2} = 5 - 2

= 5 - 2

(- 15) (- 75)

34 \cdot 2

2 + (- 8)

\frac{20 5}{4}

What is sqrt((2-\sqrt{5))^2} ?
The solution to sqrt((2-\sqrt{5))^2} is sqrt(5)-2