What is sqrt(19-8\sqrt{3)} ?

The solution to sqrt(19-8\sqrt{3)} is 4-sqrt(3)

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simplify sqrt(19-8\sqrt{3)}

simplify

19 - 83

4 - 3

Decimal Notation

2.26794 \dots

Solution steps

19 - 83

= 3 - 83 + 16

= (3)^{2} - 83 + (16)^{2}

16 = 4

= (3)^{2} - 83 + 4^{2}

23 \cdot 4 = 83

= (3)^{2} - 23 \cdot 4 + 4^{2}

Apply Perfect Square Formula:

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

(3)^{2} - 23 \cdot 4 + 4^{2} = (3 - 4)^{2}

= (3 - 4)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(3 - 4)^{2} = (4 - 3)^{2}

= (4 - 3)^{2}

Apply radical rule:

(4 - 3)^{2} = 4 - 3

= 4 - 3

\frac{5}{4} \cdot \frac{5}{4}

4^{2} + 5^{2} = x^{2}

3 (2 - x) < 14 + x

6 a = 26 + 4 a

5 x^{3} - 40 y^{3}