Trigonometry Examples

$4 \sqrt{18 k^{3} - \sqrt{72 k^{3} + \sqrt{50 k^{3}}}}$

Step 1

Apply basic rules of exponents.

Tap for more steps...

Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{50 k^{3}}$ as ${(50 k^{3})}^{\frac{1}{2}}$ .

$4 \sqrt{18 k^{3} - \sqrt{72 k^{3} + {(50 k^{3})}^{\frac{1}{2}}}}$

Step 1.2

Apply the product rule to $50 k^{3}$ .

$4 \sqrt{18 k^{3} - \sqrt{72 k^{3} + 50^{\frac{1}{2}} {(k^{3})}^{\frac{1}{2}}}}$

Step 1.3

Multiply the exponents in ${(k^{3})}^{\frac{1}{2}}$ .

Tap for more steps...

Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \sqrt{18 k^{3} - \sqrt{72 k^{3} + 50^{\frac{1}{2}} k^{3 (\frac{1}{2})}}}$

Step 1.3.2

Combine $3$ and $\frac{1}{2}$ .

$4 \sqrt{18 k^{3} - \sqrt{72 k^{3} + 50^{\frac{1}{2}} k^{\frac{3}{2}}}}$

Step 2

Factor $k^{\frac{3}{2}}$ out of $72 k^{3} + 50^{\frac{1}{2}} k^{\frac{3}{2}}$ .

Tap for more steps...

Step 2.1

Factor $k^{\frac{3}{2}}$ out of $72 k^{3}$ .

$4 \sqrt{18 k^{3} - \sqrt{k^{\frac{3}{2}} (72 k^{\frac{3}{2}}) + 50^{\frac{1}{2}} k^{\frac{3}{2}}}}$

Step 2.2

Factor $k^{\frac{3}{2}}$ out of $50^{\frac{1}{2}} k^{\frac{3}{2}}$ .

$4 \sqrt{18 k^{3} - \sqrt{k^{\frac{3}{2}} (72 k^{\frac{3}{2}}) + k^{\frac{3}{2}} \cdot 50^{\frac{1}{2}}}}$

Step 2.3

Factor $k^{\frac{3}{2}}$ out of $k^{\frac{3}{2}} (72 k^{\frac{3}{2}}) + k^{\frac{3}{2}} \cdot 50^{\frac{1}{2}}$ .

$4 \sqrt{18 k^{3} - \sqrt{k^{\frac{3}{2}} (72 k^{\frac{3}{2}} + 50^{\frac{1}{2}})}}$