What is 2(pi/3*2sqrt(3)) ?

The solution to 2(pi/3*2sqrt(3)) is (4pi)/(sqrt(3))

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simplify 2(pi/3*2sqrt(3))

simplify

2 (\frac{π}{3} \cdot 23)

\frac{4 π}{3}

Decimal Notation

7.25519 \dots

Solution steps

2 (\frac{π}{3} \cdot 23)

Apply exponent rule:

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

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

= \frac{π}{3} \cdot 2^{1 + 1} 3

Add the numbers:

1 + 1 = 2

= \frac{π}{3} \cdot 2^{2} 3

Multiply fractions:

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

= \frac{π 2 ^{2} 3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{2 ^{2} \cdot 3 ^{\frac{1}{2}} π}{3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2 ^{2} π}{3 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2 ^{2} π}{3 ^{\frac{1}{2}}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= \frac{2 ^{2} π}{3}

2^{2} = 4

= \frac{4 π}{3}

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