What is sqrt((1-\sqrt{2))}^2 ?

The solution to sqrt((1-\sqrt{2))}^2 is 1-sqrt(2)

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simplify sqrt((1-\sqrt{2))}^2

simplify

(1 - 2)^{2}

1 - 2

Decimal Notation

- 0.41421 \dots

Solution steps

(1 - 2)^{2}

Apply rule:

(a) = a

(1 - 2) = 1 - 2

= (1 - 2)^{2}

1 - 2 = - 1 + 2 i

= (- 1 + 2 i)^{2}

Apply exponent rule:

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

(- 1 + 2 i)^{2} = (- 1 + 2)^{2} i^{2}

= (- 1 + 2)^{2} i^{2}

Apply exponent rule:

(- 1 + 2)^{2} = - 1 + 2

= (- 1 + 2) i^{2}

Apply imaginary number rule:

i^{2} = - 1

= (- 1 + 2) (- 1)

Apply rule:

a (- b) = - ab

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

= - (- 1 + 2) \cdot 1

Apply rule:

a \cdot 1 = a

= - (- 1 + 2)

Apply the distributive law:

- (- a + b) = a - b

- (- 1 + 2) = 1 - 2

= 1 - 2

(x - 4) (3 x^{2} + 4 x - 4) (x - 4) (3 x^{2} + 4 x - 4)

\frac{t}{2} e^{- (\frac{t - 2}{2})} u (\frac{t - 2}{2})

(2 x) (3 x^{3}) (4 x^{2})

x 2

What is sqrt((1-\sqrt{2))}^2 ?
The solution to sqrt((1-\sqrt{2))}^2 is 1-sqrt(2)