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)