What is sqrt(2)(6+sqrt(12)) ?

The solution to sqrt(2)(6+sqrt(12)) is (6+2sqrt(3))sqrt(2)

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simplify sqrt(2)(6+sqrt(12))

simplify

2 (6 + 12)

(6 + 23) 2

Decimal Notation

13.38426 \dots

Solution steps

2 (6 + 12)

Prime factorization of

12 : 2^{2} \cdot 3

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

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

2^{2} \cdot 3 = 2^{2} 3

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

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 2 (6 + 23)

= (6 + 23) 2

(x - 5) (4 x^{2} - 2 x + 1)

4 (8 x + 1) - 6 (1 - 8 x)

\frac{1}{1 + 4 i} + \frac{1}{1 + 5 i}

32.5

\frac{1}{10} + \frac{2}{5}

What is sqrt(2)(6+sqrt(12)) ?
The solution to sqrt(2)(6+sqrt(12)) is (6+2sqrt(3))sqrt(2)