What is sqrt(2+2\sqrt{4+2\sqrt{3)}} ?

The solution to sqrt(2+2\sqrt{4+2\sqrt{3)}} is sqrt(3)+1

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simplify sqrt(2+2\sqrt{4+2\sqrt{3)}}

simplify

2 + 2 4 + 23

3 + 1

Decimal Notation

2.73205 \dots

Solution steps

2 + 2 4 + 23

2 + 2 4 + 23 = 4 + 23

= 4 + 23

= 3 + 23 + 1

= (3)^{2} + 23 + (1)^{2}

1 = 1

= (3)^{2} + 23 + 1^{2}

23 \cdot 1 = 23

= (3)^{2} + 23 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(3)^{2} + 23 \cdot 1 + 1^{2} = (3 + 1)^{2}

= (3 + 1)^{2}

Apply radical rule:

(3 + 1)^{2} = 3 + 1

= 3 + 1

12 \times 2

lo g_{3} (3^{x})

\frac{9}{4} + \frac{8}{12}

- 3 i (4 + 2 i)

(- 11 + i) 2

What is sqrt(2+2\sqrt{4+2\sqrt{3)}} ?
The solution to sqrt(2+2\sqrt{4+2\sqrt{3)}} is sqrt(3)+1