Question

$sqrt{12 div sqrt{27} }$

Answer 1

$sqrt{12 div sqrt{27} } = sqrt{ frac{12}{ sqrt{27} } } = sqrt{ frac{12}{ sqrt{9 times 3} } } = sqrt{ frac{12}{3 sqrt{3} } } = sqrt{ frac{4}{ sqrt{3} } } = sqrt{ frac{4 sqrt{3} }{3} } = frac{ sqrt{4 sqrt{3} } }{ sqrt{3} } = frac{2 sqrt{ sqrt{3} } }{ sqrt{3} } = frac{2 sqrt[4]{3} }{ sqrt{3} } = frac{2 sqrt[4]{3} sqrt{3} }{ sqrt{3} } = frac{2 sqrt[4]{3} sqrt[4]{3 {}^{2} } }{3} = frac{2 sqrt[4]{3 times 3 {}^{2} } }{3} = frac{2 sqrt[4]{3 {}^{3} } }{3} = frac{2 sqrt[4]{27} }{3}$

Answer 2

√(12:√27)=√(12:3√3)=√(4/√3)=

2•√(1/√3)==2•⁴√(1/3)