What is sqrt((2-\sqrt{7))}^2 ?

The solution to sqrt((2-\sqrt{7))}^2 is 2-sqrt(7)

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simplify sqrt((2-\sqrt{7))}^2

simplify

(2 - 7)^{2}

2 - 7

Decimal Notation

- 0.64575 \dots

Solution steps

(2 - 7)^{2}

Apply rule:

(a) = a

(2 - 7) = 2 - 7

= (2 - 7)^{2}

2 - 7 = - 2 + 7 i

= (- 2 + 7 i)^{2}

Apply exponent rule:

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

(- 2 + 7 i)^{2} = (- 2 + 7)^{2} i^{2}

= (- 2 + 7)^{2} i^{2}

Apply exponent rule:

(- 2 + 7)^{2} = - 2 + 7

= (- 2 + 7) i^{2}

Apply imaginary number rule:

i^{2} = - 1

= (- 2 + 7) (- 1)

Apply rule:

a (- b) = - ab

(- 2 + 7) (- 1) = - (- 2 + 7) \cdot 1

= - (- 2 + 7) \cdot 1

Apply rule:

a \cdot 1 = a

= - (- 2 + 7)

Apply the distributive law:

- (- a + b) = a - b

- (- 2 + 7) = 2 - 7

= 2 - 7

(\frac{5}{8})^{2}

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

What is sqrt((2-\sqrt{7))}^2 ?
The solution to sqrt((2-\sqrt{7))}^2 is 2-sqrt(7)