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Popular >

simplify 2pi(2)(4sqrt(8))

Solution

simplify

2 π (2) (48)

Solution

322 π

+1

Decimal Notation

142.17225 \dots

Solution steps

2 π (2) (48)

Apply exponent rule:

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

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

= π 2^{1 + 1} \cdot 48

Add the numbers:

1 + 1 = 2

= π 2^{2} \cdot 48

Factor integer

4 = 2^{2}

= π 2^{2} \cdot 2^{2} 8

Factor integer

8 = 2^{3}

= π 2^{2} \cdot 2^{2} 2^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

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

Refine

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

Apply exponent rule:

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

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

= π 2^{2 + 2 + \frac{3}{2}}

2^{2 + 2 + \frac{3}{2}} = 2^{5} 2

= 2^{5} 2 π

2^{5} = 32

= 322 π

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Frequently Asked Questions (FAQ)

What is 2pi(2)(4sqrt(8)) ?
The solution to 2pi(2)(4sqrt(8)) is 32sqrt(2)pi