Evaluate 2 square root of 3( square root of 18- square root of 6)

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Trigonometry

$2 \sqrt{3} (\sqrt{18} - \sqrt{6})$

Simplify each term.

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Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$2 \sqrt{3} (\sqrt{9 (2)} - \sqrt{6})$

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{3} (\sqrt{3^{2} \cdot 2} - \sqrt{6})$

Pull terms out from under the radical.

$2 \sqrt{3} (3 \sqrt{2} - \sqrt{6})$

Apply the distributive property.

$2 \sqrt{3} (3 \sqrt{2}) + 2 \sqrt{3} (- \sqrt{6})$

Multiply $2 \sqrt{3} (3 \sqrt{2})$ .

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Multiply $3$ by $2$ .

$6 \sqrt{3} \sqrt{2} + 2 \sqrt{3} (- \sqrt{6})$

Combine using the product rule for radicals.

$6 \sqrt{2 \cdot 3} + 2 \sqrt{3} (- \sqrt{6})$

Multiply $2$ by $3$ .

$6 \sqrt{6} + 2 \sqrt{3} (- \sqrt{6})$

Multiply $2 \sqrt{3} (- \sqrt{6})$ .

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Multiply $- 1$ by $2$ .

$6 \sqrt{6} - 2 \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$6 \sqrt{6} - 2 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$6 \sqrt{6} - 2 \sqrt{18}$

Simplify each term.

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Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$6 \sqrt{6} - 2 \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$6 \sqrt{6} - 2 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{6} - 2 (3 \sqrt{2})$

Multiply $3$ by $- 2$ .

$6 \sqrt{6} - 6 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{6} - 6 \sqrt{2}$

Decimal Form:

$6.21165708 \dots$

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Name

Name	one billion nine hundred twenty-four million six hundred eight thousand six hundred thirty-seven

Interesting facts

1924608637 has 4 divisors, whose sum is 2199552736
The reverse of 1924608637 is 7368064291
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 46
Digital Root 1

Name

Name	four hundred sixty-eight million seven hundred three thousand six hundred two

Interesting facts

468703602 has 32 divisors, whose sum is 1250907840
The reverse of 468703602 is 206307864
Previous prime number is 1289

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 36
Digital Root 9

Name

Name	seven hundred forty-six million six hundred forty-nine thousand seven hundred sixty

Interesting facts

746649760 has 512 divisors, whose sum is 6986887632
The reverse of 746649760 is 067946647
Previous prime number is 61

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 49
Digital Root 4

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