Question

simplify the following radical expression

Answer 1

Answer:

$2\sqrt{6} -13\sqrt{3} +4\sqrt{2}$

Step-by-step explanation:

$\sqrt{24} -5\sqrt{12} +4\sqrt{2} -3\sqrt{3}$

$=\sqrt{4\times 6} -5\sqrt{4\times 3} +4\sqrt{2} -3\sqrt{3}$

$=\sqrt{4} \times \sqrt{6} -5\times\sqrt{4} \times \sqrt{3} +4\sqrt{2} -3\sqrt{3}$

$=2\sqrt{6} -5\times2\sqrt{3} +4\sqrt{2} -3\sqrt{3}$

$=2\sqrt{6} -10\sqrt{3} +4\sqrt{2} -3\sqrt{3}$

$=2\sqrt{6} -13\sqrt{3} +4\sqrt{2}$

Answer 2

Answer:

$\boxed{ \tt 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} }$

or

$\boxed{ \tt \approx - 12.1}$

Step-by-step explanation:

Simplify:

$= \tt \sqrt{ {2}^{2} \times 6} −5 \sqrt{12} +4√2−3√3$

$= \tt \: 2 \sqrt{6} - 5 \sqrt{12} + 4 \sqrt{2 } - 3 \sqrt{3}$

$= \tt2 \sqrt{6} - \sqrt{ {2}^{2} \times 3} + 4 \sqrt{2} - 3 \sqrt{3}$

$= \tt \: 2√6−5(2√3)+4√2−3√3$

$\tt = 2√6−10√3+4√2−3√3$

$\tt = 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2}$

$\tt \approx \: - 12.1$

$\rule{225pt}{2pt}$