The square root of -8 times the square root of -40 √( - 8) * √( - 40)

Question

The square root of -8 times the square root of -40


`√( - 8) * √( - 40)`

Answer 1

The answer is: " -8 √5 " .
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Note:
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√-8 *√-40 = i√8 * i√40 ; {since: "i" refers to the imaginary number; " √-1 " } ;

= i² * √8 *√40 ;
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Note:

"√8 * √40 = ? " ;

↔ " √8 = √4 √2 = 2√2 " ;

"√40 = √4 √10 = 2√10" ;

→ "√8 √40 = 2 * 2 * √2 * √10 ;

= 4 * √(2*10) ;

= 4 √20 ;

→ " √20 = √4 √5 = 2√5 ;

→ 4 √20 = 4 * 2 * √5

= 8 √5 ;

→ i² * 8 √5 ;

↔ 8 i² √5 ;

Note: " i² = -1" ;

→ 8(-1) * √5 ;

= -8 √5 .
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