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

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

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

simplify

(1 - 2)^{2}

2 - 1

Decimal Notation

0.41421 \dots

Solution steps

(1 - 2)^{2}

(1 - 2)^{2} = 3 - 22

= 3 - 22

= 2 - 22 + 1

= (2)^{2} - 22 + (1)^{2}

1 = 1

= (2)^{2} - 22 + 1^{2}

22 \cdot 1 = 22

= (2)^{2} - 22 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(2)^{2} - 22 \cdot 1 + 1^{2} = (2 - 1)^{2}

= (2 - 1)^{2}

Apply radical rule:

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

= 2 - 1

(- 3) + (- 4)

(5 a + y)^{5}

(x + 3) (x^{2} + 3 x + 9)

(x - y) (x^{2} + y x + y^{2})

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

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