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# Simplify

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Simplify sqrt(2)*sqrt(6)*sqrt(110)*sqrt(120)*sqrt(450)*sqrt(520).

May 2, 2023

#1
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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

May 2, 2023
#2
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Pretty good! Here's another similar way.

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

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

$$\sqrt(37065600000)$$

$$100\sqrt(3706560)$$

$$800\sqrt(57915)$$

$$7200\sqrt(715)$$

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

May 2, 2023