What is sqrt(4-2\sqrt{3)} ?

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

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simplify sqrt(4-2\sqrt{3)}

simplify

4 - 23

3 - 1

Decimal Notation

0.73205 \dots

Solution steps

4 - 23

= 3 - 23 + 1

= (3)^{2} - 23 + (1)^{2}

1 = 1

= (3)^{2} - 23 + 1^{2}

23 \cdot 1 = 23

= (3)^{2} - 23 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(3)^{2} - 23 \cdot 1 + 1^{2} = (3 - 1)^{2}

= (3 - 1)^{2}

Apply radical rule:

(3 - 1)^{2} = 3 - 1

= 3 - 1

\frac{1}{1 - ( \frac{3}{2} ) ^{2}}

(- 2 - 8 i) (- 3 + 6 i)

3 (x + y)

(6 + i)^{2}

\frac{( x + 5 ) ^{2}}{5} + \frac{( y + 9 ) ^{2}}{9}