The simplified expression of [tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})[/tex]is [tex]10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}[/tex]
The expression is given as:
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})[/tex]
Expand the expression
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2\sqrt{30} \times \sqrt5+ 2\sqrt{30} \times \sqrt6+ 2\sqrt{30} \times \sqrt{10} + 2\sqrt{30} \times \sqrt{15}[/tex]
Factor out 2
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{30} \times \sqrt5+ \sqrt{30} \times \sqrt6+ \sqrt{30} \times \sqrt{10} + \sqrt{30} \times \sqrt{15})[/tex]
Combine the radicals
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{150} + \sqrt{180}+ \sqrt{300} + \sqrt{450})[/tex]
Expand the expression
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{25 \times 6} + \sqrt{9 \times 20}+ \sqrt{100 \times 3} + \sqrt{225\times 2})[/tex]
Evaluate the roots
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(5\sqrt{6} + 3\sqrt{20}+ 10\sqrt{3} + 15 \sqrt{2})[/tex]
Expand
[tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) =10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}[/tex]
Hence, the simplified expression of [tex]2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})[/tex]is [tex]10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}[/tex]
Read more about simplified expressions at:
https://brainly.com/question/8008182
