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