document.write( "Question 1036453: state the linear approximation of √99.95 \n" ); document.write( "
Algebra.Com's Answer #651164 by ikleyn(52790)\"\" \"About 
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\n" ); document.write( "state the linear approximation of sqrt(99.95)
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document.write( "\"sqrt%2899.95%29\" = \"sqrt%28100+-+0.05%29\" = \"sqrt%28100%2A%281-0.05%2F100%29%29\" = \"10%2Asqrt%281+-+0.0005%29\" = \"10%2A%281+-+0.0005%2F2%29\" = 10*(1-0.00025) = 10*0.99975 = 9.9975.\r\n" );
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document.write( "The key moment is this approximation\r\n" );
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document.write( "\"sqrt%281+-+x%29\" = \"1+-+x%2F2\" (approximately) which is valid for small values of x  (small comparatively with the value of 1).\r\n" );
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