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

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

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

simplify

(2 - 5)^{2}

2 - 5

Decimal Notation

- 0.23606 \dots

Solution steps

(2 - 5)^{2}

Apply rule:

(a) = a

(2 - 5) = 2 - 5

= (2 - 5)^{2}

2 - 5 = - 2 + 5 i

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

Apply exponent rule:

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

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

Apply imaginary number rule:

i^{2} = - 1

= (- 2 + 5) (- 1)

Apply rule:

a (- b) = - ab

(- 2 + 5) (- 1) = - (- 2 + 5) \cdot 1

= - (- 2 + 5) \cdot 1

Apply rule:

a \cdot 1 = a

= - (- 2 + 5)

Apply the distributive law:

- (- a + b) = a - b

- (- 2 + 5) = 2 - 5

= 2 - 5

(x + 1)^{- 3}

- e^{- x^{2}}

(85) \cdot 65

e^{- a t} sinh (- a t)

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