Finite Math Examples

$\sqrt{98 x^{5} y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $98 x^{5} y$ as ${(7 x^{2})}^{2} \cdot (2 x y)$ .

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Step 1.1.1

Factor $49$ out of $98$ .

$\sqrt{49 (2) x^{5} y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.2

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

$\sqrt{7^{2} \cdot 2 x^{5} y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.3

Factor out $x^{4}$ .

$\sqrt{7^{2} \cdot 2 (x^{4} x) y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.4

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

$\sqrt{7^{2} \cdot 2 ({(x^{2})}^{2} x) y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.5

Move $2$ .

$\sqrt{7^{2} {(x^{2})}^{2} \cdot 2 x y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.6

Rewrite $7^{2} {(x^{2})}^{2}$ as ${(7 x^{2})}^{2}$ .

$\sqrt{{(7 x^{2})}^{2} \cdot 2 x y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.7

Add parentheses.

$\sqrt{{(7 x^{2})}^{2} \cdot 2 (x y)} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.1.8

Add parentheses.

$\sqrt{{(7 x^{2})}^{2} \cdot (2 x y)} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.2

Pull terms out from under the radical.

$7 x^{2} \sqrt{2 x y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{4 x^{2} y^{2}}$

Step 1.3

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

$7 x^{2} \sqrt{2 x y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt[4]{{(2 x y)}^{2}}$

Step 1.4

Rewrite $\sqrt[4]{{(2 x y)}^{2}}$ as $\sqrt{\sqrt{{(2 x y)}^{2}}}$ .

$7 x^{2} \sqrt{2 x y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt{\sqrt{{(2 x y)}^{2}}}$

Step 1.5

Pull terms out from under the radical, assuming positive real numbers.

$7 x^{2} \sqrt{2 x y} + 5 x^{2} \sqrt{2 x y} - x^{2} \sqrt{2 x y}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $7 x^{2} \sqrt{2 x y}$ and $5 x^{2} \sqrt{2 x y}$ .

$12 x^{2} \sqrt{2 x y} - x^{2} \sqrt{2 x y}$

Step 2.2

Subtract $x^{2} \sqrt{2 x y}$ from $12 x^{2} \sqrt{2 x y}$ .

$11 x^{2} \sqrt{2 x y}$