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

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

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Popular >

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

simplify

13 - 43

23 - 1

Decimal Notation

2.46410 \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

15 x^{2} \times 10 x^{3}

\frac{x + 1}{3 x - 6} + \frac{5 x - 4}{6 x - 12}

\frac{16}{64}

27 - t^{3}

3 x^{3} - 2 x^{3}