What is sqrt(4-\sqrt{12)} ?

The solution to sqrt(4-\sqrt{12)} is sqrt(3)-1

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simplify sqrt(4-\sqrt{12)}

simplify

4 - 12

3 - 1

Decimal Notation

0.73205 \dots

Solution steps

4 - 12

12 = 23

= 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

(m^{3})^{5}

50 x^{3} y

(y^{3} + 1) - [(y^{2} + 1) + (3 y - 2)]

- 5 x + 6 x

x^{3} y - 81 x y