Question

Making use of the cub e root table, find the cube root s of the (correct to three decimal places)
5112

Answer 1

$3\sqrt{5112}=3\sqrt{2\times 2\times 2\times 639}=23639=23\sqrt{63.9\times 10}=2\times 3\sqrt{63.9}\times 3\sqrt{10}$
Now, from the table
$3\sqrt{63}=3.979and3\sqrt{64}=4.000\therefore Differenceafter64-63=4.000-3.979=0.021\therefore Differenceafter9=0.021\times 0.9=0.0189\therefore 3\sqrt{63.9}=3.979+0.0189=3.9979and3\sqrt{5112}=2\times \sqrt{10}\times \sqrt{63.9}=2\times 2.154\times 3.9979=17.2229=17.223$