Algebra Examples

$x \sqrt{63 x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1

Rewrite $63 x^{2}$ as ${(3 x)}^{2} \cdot 7$ .

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Step 1.1

Factor $9$ out of $63$ .

$x \sqrt{9 (7) x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1.2

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

$x \sqrt{3^{2} \cdot 7 x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1.3

Move $7$ .

$x \sqrt{3^{2} x^{2} \cdot 7} + 4 \sqrt{63 x^{4}}$

Step 1.4

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

$x \sqrt{{(3 x)}^{2} \cdot 7} + 4 \sqrt{63 x^{4}}$

Step 2

Pull terms out from under the radical.

$x (| 3 x | \sqrt{7}) + 4 \sqrt{63 x^{4}}$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{7} x | 3 x | + 4 \sqrt{63 x^{4}}$

Step 4

Remove non-negative terms from the absolute value.

$\sqrt{7} x (3 | x |) + 4 \sqrt{63 x^{4}}$

Step 5

Rewrite $63 x^{4}$ as ${(3 x^{2})}^{2} \cdot 7$ .

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Step 5.1

Factor $9$ out of $63$ .

$\sqrt{7} x (3 | x |) + 4 \sqrt{9 (7) x^{4}}$

Step 5.2

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

$\sqrt{7} x (3 | x |) + 4 \sqrt{3^{2} \cdot 7 x^{4}}$

Step 5.3

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

$\sqrt{7} x (3 | x |) + 4 \sqrt{3^{2} \cdot 7 {(x^{2})}^{2}}$

Step 5.4

Move $7$ .

$\sqrt{7} x (3 | x |) + 4 \sqrt{3^{2} {(x^{2})}^{2} \cdot 7}$

Step 5.5

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

$\sqrt{7} x (3 | x |) + 4 \sqrt{{(3 x^{2})}^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$\sqrt{7} x (3 | x |) + 4 (| 3 x^{2} | \sqrt{7})$

Step 7

Remove non-negative terms from the absolute value.

$\sqrt{7} x (3 | x |) + 4 (3 x^{2} \sqrt{7})$

Step 8

Multiply $3$ by $4$ .

$\sqrt{7} x \cdot 3 | x | + 12 x^{2} \sqrt{7}$