What is sqrt(29-12\sqrt{5)} ?

The solution to sqrt(29-12\sqrt{5)} is 2sqrt(5)-3

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simplify sqrt(29-12\sqrt{5)}

simplify

29 - 125

25 - 3

Decimal Notation

1.47213 \dots

Solution steps

29 - 125

= 20 - 125 + 9

= 4 \cdot 5 - 125 + 9

= (4)^{2} (5)^{2} - 125 + (9)^{2}

4 = 2

9 = 3

= 2^{2} (5)^{2} - 125 + 3^{2}

2 \cdot 25 \cdot 3 = 125

= (25)^{2} - 2 \cdot 25 \cdot 3 + 3^{2}

Apply Perfect Square Formula:

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

(25)^{2} - 2 \cdot 25 \cdot 3 + 3^{2} = (25 - 3)^{2}

= (25 - 3)^{2}

Apply radical rule:

(25 - 3)^{2} = 25 - 3

= 25 - 3

(\frac{3}{8} + \frac{5}{12})^{- 1}

tan^{2} (x) + 1

\frac{1}{tan ( x )}

\frac{sin ^{2} ( x )}{cos ^{2} ( x )}

\frac{1}{2} x^{4} - (x + 1)^{3} - 3 x^{2}