What is sqrt((\sqrt{27)-(2sqrt(12)+sqrt(6)))}^2 ?

The solution to sqrt((\sqrt{27)-(2sqrt(12)+sqrt(6)))}^2 is -sqrt(3)-sqrt(6)

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Popular >

simplify sqrt((\sqrt{27)-(2sqrt(12)+sqrt(6)))}^2

simplify

(27 - (212 + 6))^{2}

- 3 - 6

Decimal Notation

- 4.18154 \dots

Solution steps

(27 - (212 + 6))^{2}

Apply rule:

(a) = a

(27 - (212 + 6)) = 27 - (212 + 6)

= (27 - (212 + 6))^{2}

27 - (212 + 6) = 3 + 6 i

= (3 + 6 i)^{2}

Apply exponent rule:

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

(3 + 6 i)^{2} = (3 + 6)^{2} i^{2}

= (3 + 6)^{2} i^{2}

Apply exponent rule:

(3 + 6)^{2} = 3 + 6

= (3 + 6) i^{2}

Apply imaginary number rule:

i^{2} = - 1

= (3 + 6) (- 1)

Apply rule:

a (- b) = - ab

(3 + 6) (- 1) = - (3 + 6) \cdot 1

= - (3 + 6) \cdot 1

Apply rule:

a \cdot 1 = a

= - (3 + 6)

Apply the distributive law:

- (a + b) = - a - b

- (3 + 6) = - 3 - 6

= - 3 - 6

(201)^{2}

(\frac{6}{5})^{2}

What is sqrt((\sqrt{27)-(2sqrt(12)+sqrt(6)))}^2 ?
The solution to sqrt((\sqrt{27)-(2sqrt(12)+sqrt(6)))}^2 is -sqrt(3)-sqrt(6)