Simplify

The simplification of the given expression is equal to 192524.3.

Step-by-step explanation:

The expression is equal to,

√2 × √6 × √110 × √120 × √450 × √520

Simplify this expression by first simplifying the square roots under the radical signs,

√2 = √(2 × 1) 

     = √2 × √1

√6 = √(2 × 3) 

     = √2 × √3

√110 = √(2 × 5 × 11) 

        = √2 × √5 × √11

√120 = √(2 × 2 × 2 × 3 × 5) 

        = 2√2 × √3 × √5

√450 = √(2 × 3² × 5²) 

         = √2 × (3 × 5)² 

         = 15√2 

√520 = √(2³ × 5 × 13) 

        = 2√2 ×√5 × √13

Substituting these simplifications back into the original expression, we have,

√2 × √6 × √110 × √120 × √450 × √520

= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2  ×  2√2 ×√5 × √13

= 2⁵ × 3² × 5²√(5 × 11  × 13)

= 7200√715

= 192524.3

Pretty good! Here's another similar way.

\(\sqrt(2)*\sqrt(6)*\sqrt(110)*\sqrt(120)*\sqrt(450)*\sqrt(520)\)

\(\sqrt(2*6*110*120*450*520)\)

\(\sqrt(37065600000)\)

\(100\sqrt(3706560)\)

\(800\sqrt(57915)\)

\(7200\sqrt(715)\)

\(7200*\sqrt(5)*\sqrt(11)*\sqrt(13)\)