What is \sqrt[6]{(2944)^3} ?

The solution to \sqrt[6]{(2944)^3} is 8sqrt(46)

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simplify \sqrt[6]{(2944)^3}

simplify

846

Decimal Notation

54.25863 \dots

Solution steps

Apply radical rule:

= ((2944)^{3})^{\frac{1}{6}}

Apply exponent rule:

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

= (2944)^{3 \cdot \frac{1}{6}}

3 \cdot \frac{1}{6} = \frac{1}{2}

= (2944)^{\frac{1}{2}}

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

= 2944

Prime factorization of

2944 : 2^{7} \cdot 23

= 2^{7} \cdot 23

Apply exponent rule:

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

= 2^{6} \cdot 2 \cdot 23

Apply radical rule:

= 2^{6} 2 \cdot 23

Apply radical rule:

2^{6} = 2^{\frac{6}{2}} = 2^{3}

= 2^{3} 2 \cdot 23

Refine

= 846

7.2 x 1 0^{- 3}

0.1 \cdot 2^{- 2}

0.1 \cdot 2^{- 4}

7.61 \cdot 1 0^{- 2}

2 (42)