Simplify square root of 338x^6y^3z^4+ square root of 288x^6y^3z^4

$\sqrt{338 x^{6} y^{3} z^{4}} + \sqrt{288 x^{6} y^{3} z^{4}}$

Simplify each term.

Rewrite $338 x^{6} y^{3} z^{4}$ as ${(13 x^{3} y z^{2})}^{2} \cdot (2 y)$ .

Factor $169$ out of $338$ .

$\sqrt{169 (2) x^{6} y^{3} z^{4}} + \sqrt{288 x^{6} y^{3} z^{4}}$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2} \cdot 2 x^{6} y^{3} z^{4}} + \sqrt{288 x^{6} y^{3} z^{4}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{13^{2} \cdot 2 {(x^{3})}^{2} y^{3} z^{4}} + \sqrt{288 x^{6} y^{3} z^{4}}$

Factor out $y^{2}$ .

$\sqrt{13^{2} \cdot 2 {(x^{3})}^{2} (y^{2} y) z^{4}} + \sqrt{288 x^{6} y^{3} z^{4}}$

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

$\sqrt{13^{2} \cdot 2 {(x^{3})}^{2} (y^{2} y) {(z^{2})}^{2}} + \sqrt{288 x^{6} y^{3} z^{4}}$

Move $y$ .

$\sqrt{13^{2} \cdot 2 {(x^{3})}^{2} (y^{2}) {(z^{2})}^{2} y} + \sqrt{288 x^{6} y^{3} z^{4}}$

Move $2$ .

$\sqrt{(13^{2} {(x^{3})}^{2} (y^{2})) {(z^{2})}^{2} \cdot 2 y} + \sqrt{288 x^{6} y^{3} z^{4}}$

Rewrite $(13^{2} {(x^{3})}^{2} (y^{2})) {(z^{2})}^{2}$ as ${(13 x^{3} y z^{2})}^{2}$ .

$\sqrt{{(13 x^{3} y z^{2})}^{2} \cdot 2 y} + \sqrt{288 x^{6} y^{3} z^{4}}$

Add parentheses.

$\sqrt{{(13 x^{3} y z^{2})}^{2} \cdot (2 y)} + \sqrt{288 x^{6} y^{3} z^{4}}$

Pull terms out from under the radical.

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{288 x^{6} y^{3} z^{4}}$

Rewrite $288 x^{6} y^{3} z^{4}$ as ${(12 x^{3} y z^{2})}^{2} \cdot (2 y)$ .

Factor $144$ out of $288$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{144 (2) x^{6} y^{3} z^{4}}$

Rewrite $144$ as $12^{2}$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{12^{2} \cdot 2 x^{6} y^{3} z^{4}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{12^{2} \cdot 2 {(x^{3})}^{2} y^{3} z^{4}}$

Factor out $y^{2}$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{12^{2} \cdot 2 {(x^{3})}^{2} (y^{2} y) z^{4}}$

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

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{12^{2} \cdot 2 {(x^{3})}^{2} (y^{2} y) {(z^{2})}^{2}}$

Move $y$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{12^{2} \cdot 2 {(x^{3})}^{2} (y^{2}) {(z^{2})}^{2} y}$

Move $2$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{12^{2} {(x^{3})}^{2} (y^{2}) {(z^{2})}^{2} \cdot 2 y}$

Rewrite $(12^{2} {(x^{3})}^{2} (y^{2})) {(z^{2})}^{2}$ as ${(12 x^{3} y z^{2})}^{2}$ .

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{{(12 x^{3} y z^{2})}^{2} \cdot 2 y}$

Add parentheses.

$13 x^{3} y z^{2} \sqrt{2 y} + \sqrt{{(12 x^{3} y z^{2})}^{2} \cdot (2 y)}$

Pull terms out from under the radical.

$13 x^{3} y z^{2} \sqrt{2 y} + 12 x^{3} y z^{2} \sqrt{2 y}$

Add $13 x^{3} y z^{2} \sqrt{2 y}$ and $12 x^{3} y z^{2} \sqrt{2 y}$ .

$25 x^{3} y z^{2} \sqrt{2 y}$

Simplify square root of 338x^6y^3z^4+ square root of 288x^6y^3z^4

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