What is the value of sqrt(2^2+2^2-2(2*2)cos(30)) ?

The value of sqrt(2^2+2^2-2(2*2)cos(30)) is 2sqrt(2-\sqrt{3)}

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sqrt(2^2+2^2-2(2*2)cos(30))

2^{2} + 2^{2} - 2 (2 \cdot 2) cos (3 0^{\circ})

2 2 - 3

Decimal Notation

1.03527 \dots

Solution steps

2^{2} + 2^{2} - 2 (2 \cdot 2) cos (3 0^{\circ})

= 2^{2} + 2^{2} - 2 \cdot 2 \cdot 2 cos (3 0^{\circ})

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 2^{2} + 2^{2} - 2 \cdot 2 \cdot 2 \cdot \frac{3}{2}

Simplify

2^{2} + 2^{2} - 2 \cdot 2 \cdot 2 \cdot \frac{3}{2} : 2 2 - 3

2^{2} + 2^{2} - 2 \cdot 2 \cdot 2 \cdot \frac{3}{2}

Add similar elements:

2^{2} + 2^{2} = 2^{2} \cdot 2

= 2^{2} \cdot 2 - 2 \cdot 2 \cdot 2 \cdot \frac{3}{2}

2 \cdot 2^{2} = 2^{3}

2 \cdot 2^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2^{2} = 2^{1 + 2}

= 2^{1 + 2}

Add the numbers:

1 + 2 = 3

= 2^{3}

2 \cdot 2 \cdot 2 \cdot \frac{3}{2} = 43

2 \cdot 2 \cdot 2 \cdot \frac{3}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 2 \cdot 2 \cdot 2}{2}

Cancel the common factor:

2

= 3 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 43

= 2^{3} - 43

Factor

2^{3} - 43 : 4 (2 - 3)

2^{3} - 43

Rewrite as

= 4 \cdot 2 - 43

Factor out common term

4

= 4 (2 - 3)

= 4 (2 - 3)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 2 - 3

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= 2 2 - 3

= 2 2 - 3

cos (2 \cdot 180)

sin (5 3^{\circ}) \cdot 100

arctan (\frac{7}{2.4})

cos (2 (45))

\frac{12}{tan ( 23.9 7 ^{\circ} )}

What is the value of sqrt(2^2+2^2-2(2*2)cos(30)) ?
The value of sqrt(2^2+2^2-2(2*2)cos(30)) is 2sqrt(2-\sqrt{3)}