What is sqrt(39+12\sqrt{3)} ?

The solution to sqrt(39+12\sqrt{3)} is sqrt(3)+6

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simplify sqrt(39+12\sqrt{3)}

simplify

39 + 123

3 + 6

Decimal Notation

7.73205 \dots

Solution steps

39 + 123

= 3 + 123 + 36

= (3)^{2} + 123 + (36)^{2}

36 = 6

= (3)^{2} + 123 + 6^{2}

23 \cdot 6 = 123

= (3)^{2} + 23 \cdot 6 + 6^{2}

Apply Perfect Square Formula:

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

(3)^{2} + 23 \cdot 6 + 6^{2} = (3 + 6)^{2}

= (3 + 6)^{2}

Apply radical rule:

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

= 3 + 6

(3^{n}) (1 0^{n})

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

a \cdot (- 1)

\frac{( x + 2 ) ^{2} - 4}{x}

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