The answer is: " 1120 " .
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Given: " 3√⋅2√2⋅5√8⋅√18 " ;
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→ 3√⋅2√2⋅5√8⋅√18 = 3*2*5*√2*√2*√8*18;
Consider "√8" ;
→ √8 = √4 * √2 = 2 √2 ;
Consider: "√18" ;
→ √18 = √9 * √2 = 3 √2 ;
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So; → " 3*2*5*√2*√2*√8*18 "
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Rewrite, substitute: "2*√2" for "√8" ;
and: substitute: "3*√2" for "√18" ;
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→ " 3*2*5*√2*√2*2*√2*3*√2"
= 3*2*5*2*3*√2*√2*√2*√2 ;
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Note: Since: "√2*√2 = "2" ;
→ "√2*√2*√2*√2 = 2 * 2 = 4 ;
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So; 3*2*5*2*3*√2*√2*√2*√2 ;
= 3*2*5*2*3*4 ;
3*2 = 6 ;
6* 5 = 30;
30 * 2 = 60 ;
60 * 3 = 180 ;
180 * 4 = 1120 .
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The answer is: " 1120 " .
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