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

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

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

simplify

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

6 + 3

Decimal Notation

4.18154 \dots

Solution steps

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

(27 - (212 + 6))^{2} = 9 + 62

= 9 + 62

= 6 + 62 + 3

= 3 \cdot 2 + 62 + 3

= (3)^{2} (2)^{2} + 62 + (3)^{2}

2323 = 62

= (32)^{2} + 2323 + (3)^{2}

Apply Perfect Square Formula:

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

(32)^{2} + 2323 + (3)^{2} = (32 + 3)^{2}

= (32 + 3)^{2}

Apply radical rule:

(32 + 3)^{2} = 32 + 3

= 32 + 3

32 = 6

= 6 + 3

(x + 5) (x^{2} + 3 x - 1)

f^{- 1} (4)

\frac{x}{2} + 1

- (\frac{1}{3})^{4}

2 \cdot 15

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