Finite Math Examples

$6 r \sqrt{27 r^{2} s} - 3 r^{2} \sqrt{3 s}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27 r^{2} s$ as ${(3 r)}^{2} \cdot (3 s)$ .

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Step 1.1.1

Factor $9$ out of $27$ .

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

Step 1.1.2

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

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

Step 1.1.3

Move $3$ .

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

Step 1.1.4

Rewrite $3^{2} r^{2}$ as ${(3 r)}^{2}$ .

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

Step 1.1.5

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $r$ by $r$ by adding the exponents.

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Step 1.3.1

Move $r$ .

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

Step 1.3.2

Multiply $r$ by $r$ .

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

Step 1.4

Multiply $3$ by $6$ .

$18 r^{2} \sqrt{3 s} - 3 r^{2} \sqrt{3 s}$

Step 2

Subtract $3 r^{2} \sqrt{3 s}$ from $18 r^{2} \sqrt{3 s}$ .

$15 r^{2} \sqrt{3 s}$