Linear Algebra Examples

$\frac{\sqrt{45 x^{3} y^{4}}}{\sqrt{16 x}}$

Step 1

Combine $\sqrt{45 x^{3} y^{4}}$ and $\sqrt{16 x}$ into a single radical.

$\sqrt{\frac{45 x^{3} y^{4}}{16 x}}$

Step 2

Reduce the expression $\frac{45 x^{3} y^{4}}{16 x}$ by cancelling the common factors.

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Step 2.1

Factor $x$ out of $45 x^{3} y^{4}$ .

$\sqrt{\frac{x (45 x^{2} y^{4})}{16 x}}$

Step 2.2

Factor $x$ out of $16 x$ .

$\sqrt{\frac{x (45 x^{2} y^{4})}{x \cdot 16}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{x (45 x^{2} y^{4})}{x \cdot 16}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{45 x^{2} y^{4}}{16}}$

Step 3

Rewrite $\frac{45 x^{2} y^{4}}{16}$ as ${(\frac{3 x y^{2}}{4})}^{2} \cdot 5$ .

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Step 3.1

Factor the perfect power ${(3 x y^{2})}^{2}$ out of $45 x^{2} y^{4}$ .

$\sqrt{\frac{{(3 x y^{2})}^{2} \cdot 5}{16}}$

Step 3.2

Factor the perfect power $4^{2}$ out of $16$ .

$\sqrt{\frac{{(3 x y^{2})}^{2} \cdot 5}{4^{2} \cdot 1}}$

Step 3.3

Rearrange the fraction $\frac{{(3 x y^{2})}^{2} \cdot 5}{4^{2} \cdot 1}$ .

$\sqrt{{(\frac{3 x y^{2}}{4})}^{2} \cdot 5}$

Step 4

Pull terms out from under the radical.

$\frac{3 x y^{2}}{4} \sqrt{5}$

Step 5

Combine $\frac{3 x y^{2}}{4}$ and $\sqrt{5}$ .

$\frac{3 x y^{2} \sqrt{5}}{4}$