1.) [tex] \sqrt{228,000,000 ^{3} } [/tex]
= [tex]( \sqrt{228 ^{3} } )( \sqrt{1,000,000 ^{3} } )
[/tex]
2) Simplify [tex] \sqrt{228 ^{3} } = 228 ^{ \frac{3}{2} } [/tex]
[tex]228 ^{ \frac{3}{2} } = 228 ^{1 \frac{1}{2} } [/tex]
[tex]228 ^{1 \frac{1}{2} } = (228 ^{1} )(228 ^{ \frac{1}{2} } ) = 228 \sqrt{228} [/tex]
[tex]228 \sqrt{228} =228 \sqrt{(4)(57)} = 228(2) \sqrt{57} [/tex]
[tex]228(2) \sqrt{57} =456 \sqrt{57} [/tex]
3) Simplify [tex] \sqrt{1,000,000 ^{3} } = 1,000,000 ^{ \frac{3}{2} } [/tex]
[tex]1,000,000 ^{ \frac{3}{2} } = (1,000,000 ^{1} )(1,000,000 ^{ \frac{1}{2} } )[/tex]
[tex]1,000,000(1,000,000 ^{ \frac{1}{2} })=1,000,000 \sqrt{1,000,000} [/tex]
= [tex]1,000,000(1,000) =1,000,000,000[/tex]
4) Multiply the quantities, then simplify:
(0.000544)(456)(1,000,000,000)[tex]( \sqrt{57)} [/tex]
= (0.248064)(1,000,000,000)[tex]( \sqrt{57} )[/tex]
= (248,064,000) [tex] \sqrt{57} [/tex]
With calculator:
= (248,064,000)(7.54983443527)
= 1,872,842,129.3508
(Please use this as guide to step-by-step solution. You have posted similar problems with constant 0.000544. Hope this helps.)
