Question

What is the cube root of 590.625 ??
It is cube root not square root..
Please help!!

Answer 1

Hello!!!

$590.625 = \frac{590625}{1000} \\ \\ factorize \: the \: numerator \\ \\ = \frac{5 \times 5 \times 5 \times 5 \times 5 \times 3 \times 3 \times 3 \times 7}{ {10}^{3} } \\ \\ = \frac{5 {}^{3} \times {3}^{3} \times 25 \times 7 }{10 {}^{3} } \\ \\ take \: cube \: root \\ \\ = \sqrt[3]{ \frac{5 {}^{3} \times 3 {}^{3 }\times 175 } { {10}^{3} }} = \frac{5 \times 3 \times \sqrt[3]{175} }{10} \\ \\ = \frac{5 \times 3 \times 5.5}{10} = 8.25 \\ \\ \\ (assume \: that \: cuberoot \: of \: 175 \: is \: approximately \: 5.5 \: .....as \: it \: is \: between \: {5}^{3} and \: 6 {}^{ 3}$