document.write( "Question 211272: simplify by factoring\r
\n" ); document.write( "\n" ); document.write( "cube rt of sqrt 48x^8 \n" ); document.write( "
Algebra.Com's Answer #159637 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
First, let's simplify \"sqrt%2848x%5E8%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%2848%2Ax%5E8%29\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%2816%2A3%2Ax%5E8%29\" Factor \"48\" into \"16%2A3\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%2816%2A3%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%29\" Factor \"x%5E8\" into \"x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2\"\r
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\n" ); document.write( "\n" ); document.write( " Break up the square root using the identity \"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29\".\r
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\n" ); document.write( "\n" ); document.write( "\"4%2Asqrt%283%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29\" Take the square root of \"16\" to get \"4\".\r
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\n" ); document.write( "\n" ); document.write( "\"4%2Asqrt%283%29%2Ax%2Ax%2Ax%2Ax\" Take the square root of \"x%5E2\" to get \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E4%2Asqrt%283%29\" Rearrange and multiply the terms.\r
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\n" ); document.write( "\n" ); document.write( "So \"sqrt%2848%2Ax%5E8%29\" simplifies to \"4x%5E4%2Asqrt%283%29\"\r
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\n" ); document.write( "\n" ); document.write( "In other words, \"sqrt%2848%2Ax%5E8%29=4x%5E4%2Asqrt%283%29\" where every variable is non-negative.\r
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\n" ); document.write( "\n" ); document.write( "So \"root%283%2Csqrt%2848%2Ax%5E8%29%29\" simplifies to \"root%283%2C4x%5E4%2Asqrt%283%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "Ie. \"root%283%2Csqrt%2848%2Ax%5E8%29%29=root%283%2C4x%5E4%2Asqrt%283%29%29\" where \"x%3E=0\"\r
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\n" ); document.write( "\n" ); document.write( "Now let's simplify \"root%283%2C4x%5E4%2Asqrt%283%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C4x%5E4%2Asqrt%283%29%29\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C4x%5E4%29%2Aroot%283%2Csqrt%283%29%29\" Break up the root.\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C4x%2Ax%5E3%29%2Aroot%283%2Csqrt%283%29%29\" Factor \"x%5E4\" to get \"x%2Ax%5E3\"\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C4x%29%2Aroot%283%2Cx%5E3%29%2Aroot%283%2Csqrt%283%29%29\" Break up the first root.\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C4x%29%2Ax%2Aroot%283%2Csqrt%283%29%29\" Take the cube root of \"x%5E3\" to get \"x\"\r
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\n" ); document.write( "\n" ); document.write( "\"%284x%29%5E%281%2F3%29%5E%22%22%2Ax%2A%283%5E%281%2F2%29%29%5E%281%2F3%29\" Convert to exponential notation.\r
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\n" ); document.write( "\n" ); document.write( "\"%284x%29%5E%281%2F3%29%2Ax%2A3%5E%281%2F6%29%5E%22%22\" Multiply the exponents.\r
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\n" ); document.write( "\n" ); document.write( "\"%284x%29%5E%282%2F6%29%5E%22%22%2Ax%2A3%5E%281%2F6%29\" Rewrite the first exponent \"1%2F3\" as \"2%2F6\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%2A%28%284x%29%5E%282%2F6%29%5E%22%22%2A3%5E%281%2F6%29%29\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "\"x%2A%28%284x%29%5E2%2A3%5E1%29%5E%281%2F6%29\" Factor out \"1%2F6\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%2A%2816x%5E2%2A3%29%5E%281%2F6%29\" Square and simplify\r
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\n" ); document.write( "\n" ); document.write( "\"x%2A%2848x%5E2%29%5E%281%2F6%29\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"x%2Aroot%286%2C48x%5E2%29\" Convert back to radical notation.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So \"root%283%2Csqrt%2848%2Ax%5E8%29%29\" completely simplifies to \"x%2Aroot%286%2C48x%5E2%29\"\r
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\n" ); document.write( "\n" ); document.write( "In other words, \"root%283%2Csqrt%2848%2Ax%5E8%29%29=x%2Aroot%286%2C48x%5E2%29\" where \"x%3E=0\"\r
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