Evaluate 5 square root of 6(3 square root of 6-6 square root of 3)

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Trigonometry

$5 \sqrt{6} (3 \sqrt{6} - 6 \sqrt{3})$

Apply the distributive property.

$5 \sqrt{6} (3 \sqrt{6}) + 5 \sqrt{6} (- 6 \sqrt{3})$

Multiply $5 \sqrt{6} (3 \sqrt{6})$ .

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Multiply $3$ by $5$ .

$15 \sqrt{6} \sqrt{6} + 5 \sqrt{6} (- 6 \sqrt{3})$

Raise $\sqrt{6}$ to the power of $1$ .

$15 ({\sqrt{6}}^{1} \sqrt{6}) + 5 \sqrt{6} (- 6 \sqrt{3})$

Raise $\sqrt{6}$ to the power of $1$ .

$15 ({\sqrt{6}}^{1} {\sqrt{6}}^{1}) + 5 \sqrt{6} (- 6 \sqrt{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 {\sqrt{6}}^{1 + 1} + 5 \sqrt{6} (- 6 \sqrt{3})$

Add $1$ and $1$ .

$15 {\sqrt{6}}^{2} + 5 \sqrt{6} (- 6 \sqrt{3})$

Multiply $5 \sqrt{6} (- 6 \sqrt{3})$ .

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Multiply $- 6$ by $5$ .

$15 {\sqrt{6}}^{2} - 30 \sqrt{6} \sqrt{3}$

Combine using the product rule for radicals.

$15 {\sqrt{6}}^{2} - 30 \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$15 {\sqrt{6}}^{2} - 30 \sqrt{18}$

Simplify each term.

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Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$15 {(6^{\frac{1}{2}})}^{2} - 30 \sqrt{18}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$15 \cdot 6^{\frac{1}{2} \cdot 2} - 30 \sqrt{18}$

Combine $\frac{1}{2}$ and $2$ .

$15 \cdot 6^{\frac{2}{2}} - 30 \sqrt{18}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$15 \cdot 6^{\frac{2}{2}} - 30 \sqrt{18}$

Divide $1$ by $1$ .

$15 \cdot 6^{1} - 30 \sqrt{18}$

Evaluate the exponent.

$15 \cdot 6 - 30 \sqrt{18}$

Multiply $15$ by $6$ .

$90 - 30 \sqrt{18}$

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

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Factor $9$ out of $18$ .

$90 - 30 \sqrt{9 (2)}$

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

$90 - 30 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$90 - 30 (3 \sqrt{2})$

Multiply $3$ by $- 30$ .

$90 - 90 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$90 - 90 \sqrt{2}$

Decimal Form:

$- 37.27922061 \dots$

Do you know how to Evaluate 5 square root of 6(3 square root of 6-6 square root of 3)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	one billion eight hundred seventy-three million seven hundred sixty-three thousand eight hundred five

Interesting facts

1873763805 has 32 divisors, whose sum is 3104438400
The reverse of 1873763805 is 5083673781
Previous prime number is 29

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 48
Digital Root 3

Name

Name	one billion six hundred eighteen million seven hundred thirty-seven thousand six hundred ninety-seven

Interesting facts

1618737697 has 4 divisors, whose sum is 1640912260
The reverse of 1618737697 is 7967378161
Previous prime number is 73

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 55
Digital Root 1

Name

Name	one billion eight hundred thirty-three million two hundred sixty-eight thousand four hundred seventy-two

Interesting facts

1833268472 has 64 divisors, whose sum is 7176733056
The reverse of 1833268472 is 2748623381
Previous prime number is 67

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 44
Digital Root 8

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