Basic Math Examples

$3 \sqrt{40} (3 \sqrt{27} - 2)$

Step 1

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 1.1

Factor $4$ out of $40$ .

$3 \sqrt{4 (10)} (3 \sqrt{27} - 2)$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{2^{2} \cdot 10} (3 \sqrt{27} - 2)$

$3 \sqrt{2^{2} \cdot 10} (3 \sqrt{27} - 2)$

Step 2

Simplify by cancelling exponent with radical.

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Step 2.1

Pull terms out from under the radical.

$3 (2 \sqrt{10}) (3 \sqrt{27} - 2)$

Step 2.2

Multiply $2$ by $3$ .

$6 \sqrt{10} (3 \sqrt{27} - 2)$

$6 \sqrt{10} (3 \sqrt{27} - 2)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 3.1.1

Factor $9$ out of $27$ .

$6 \sqrt{10} (3 \sqrt{9 (3)} - 2)$

Step 3.1.2

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

$6 \sqrt{10} (3 \sqrt{3^{2} \cdot 3} - 2)$

$6 \sqrt{10} (3 \sqrt{3^{2} \cdot 3} - 2)$

Step 3.2

Pull terms out from under the radical.

$6 \sqrt{10} (3 (3 \sqrt{3}) - 2)$

Step 3.3

Multiply $3$ by $3$ .

$6 \sqrt{10} (9 \sqrt{3} - 2)$

$6 \sqrt{10} (9 \sqrt{3} - 2)$

Step 4

Apply the distributive property.

$6 \sqrt{10} (9 \sqrt{3}) + 6 \sqrt{10} \cdot - 2$

Step 5

Multiply $6 \sqrt{10} (9 \sqrt{3})$ .

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Step 5.1

Multiply $9$ by $6$ .

$54 \sqrt{10} \sqrt{3} + 6 \sqrt{10} \cdot - 2$

Step 5.2

Combine using the product rule for radicals.

$54 \sqrt{3 \cdot 10} + 6 \sqrt{10} \cdot - 2$

Step 5.3

Multiply $3$ by $10$ .

$54 \sqrt{30} + 6 \sqrt{10} \cdot - 2$

$54 \sqrt{30} + 6 \sqrt{10} \cdot - 2$

Step 6

Multiply $- 2$ by $6$ .

$54 \sqrt{30} - 12 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$54 \sqrt{30} - 12 \sqrt{10}$

Decimal Form:

$257.82284913 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$