Precalculus Examples

$5 \sqrt{98 m^{2} n^{5}} - 3 m \sqrt{16 n^{5}}$

Step 1

Rewrite $98 m^{2} n^{5}$ as ${(7 m n^{2})}^{2} \cdot (2 n)$ .

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Step 1.1

Factor $49$ out of $98$ .

$5 \sqrt{49 (2) m^{2} n^{5}} - 3 m \sqrt{16 n^{5}}$

Step 1.2

Rewrite $49$ as $7^{2}$ .

$5 \sqrt{7^{2} \cdot 2 m^{2} n^{5}} - 3 m \sqrt{16 n^{5}}$

Step 1.3

Factor out $n^{4}$ .

$5 \sqrt{7^{2} \cdot 2 m^{2} (n^{4} n)} - 3 m \sqrt{16 n^{5}}$

Step 1.4

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

$5 \sqrt{7^{2} \cdot 2 m^{2} ({(n^{2})}^{2} n)} - 3 m \sqrt{16 n^{5}}$

Step 1.5

Move $2$ .

$5 \sqrt{7^{2} m^{2} {(n^{2})}^{2} \cdot 2 n} - 3 m \sqrt{16 n^{5}}$

Step 1.6

Rewrite $7^{2} m^{2} {(n^{2})}^{2}$ as ${(7 m n^{2})}^{2}$ .

$5 \sqrt{{(7 m n^{2})}^{2} \cdot 2 n} - 3 m \sqrt{16 n^{5}}$

Step 1.7

Add parentheses.

$5 \sqrt{{(7 m n^{2})}^{2} \cdot (2 n)} - 3 m \sqrt{16 n^{5}}$

Step 2

Pull terms out from under the radical.

$5 (7 m n^{2} \sqrt{2 n}) - 3 m \sqrt{16 n^{5}}$

Step 3

Multiply $7$ by $5$ .

$35 (m n^{2} \sqrt{2 n}) - 3 m \sqrt{16 n^{5}}$

Step 4

Rewrite $16 n^{5}$ as ${(4 n^{2})}^{2} n$ .

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Step 4.1

Rewrite $16$ as $4^{2}$ .

$35 m n^{2} \sqrt{2 n} - 3 m \sqrt{4^{2} n^{5}}$

Step 4.2

Factor out $n^{4}$ .

$35 m n^{2} \sqrt{2 n} - 3 m \sqrt{4^{2} (n^{4} n)}$

Step 4.3

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

$35 m n^{2} \sqrt{2 n} - 3 m \sqrt{4^{2} ({(n^{2})}^{2} n)}$

Step 4.4

Rewrite $4^{2} {(n^{2})}^{2}$ as ${(4 n^{2})}^{2}$ .

$35 m n^{2} \sqrt{2 n} - 3 m \sqrt{{(4 n^{2})}^{2} n}$

Step 5

Pull terms out from under the radical.

$35 m n^{2} \sqrt{2 n} - 3 m (4 n^{2} \sqrt{n})$

Step 6

Multiply $4$ by $- 3$ .

$35 m n^{2} \sqrt{2 n} - 12 m n^{2} \sqrt{n}$