What is sqrt(13+4\sqrt{3)} ?

The solution to sqrt(13+4\sqrt{3)} is 2sqrt(3)+1

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simplify sqrt(13+4\sqrt{3)}

simplify

13 + 43

23 + 1

Decimal Notation

4.46410 \dots

Solution steps

13 + 43

= 12 + 43 + 1

= 4 \cdot 3 + 43 + 1

= (4)^{2} (3)^{2} + 43 + (1)^{2}

4 = 2

1 = 1

= 2^{2} (3)^{2} + 43 + 1^{2}

2 \cdot 23 \cdot 1 = 43

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

Apply Perfect Square Formula:

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

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

= (23 + 1)^{2}

Apply radical rule:

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

= 23 + 1

16 c^{4} p + 20 c p^{3}

31!

9 - 0

\frac{1}{x} \times x^{2}

x^{5} - 8 x^{3} + 16 x