Question

Multiply. √3 ⋅ 2√2 ⋅ 5√8 ⋅ √18 Enter your answer, in simplest radical form, in the box.

Answer 1

120√6

Explanation:

Simplify the 5√8 to 2√2

simplify the √18 to 3√2

so it would be √3 * 2√2 * 5 * 2√2 * 3√2

when a square root of an expression is multiplied by itself:

√3 * 2 * 2* 5 * 2 * 3√2

so as we calculate it, 2 * 2* 5 * 2 * 3 = 120 and √2 * √3 = 6

Answer 2

`\sqrt3\\2\sqrt2\\5\sqrt8=5√(4\cdot2)=5\sqrt4\cdot\sqrt2=5(2)\sqrt2=10\sqrt2\\√(18)=√(9\cdot2)=\sqrt9\cdot\sqrt2=3\sqrt2\\\\\sqrt3\cdot2\sqrt2\cdot5\sqrt8\cdot√(18)=\sqrt3\cdot2\sqrt2\cdot10\sqrt2\cdot3\sqrt2\\\\=(2\cdot10\cdot3)(\sqrt3\cdot\sqrt2\cdot\sqrt2\cdot\sqrt2)=60√(3\cdot2)\cdot√(2\cdot2)\\\\=60\sqrt6\cdot\sqrt4=60\sqrt6\cdot2=(60\cdot2)(\sqrt6)\\\\=\boxed{120\sqrt6}`