Algebra Examples

$\sqrt{8 y + 5 \sqrt{50 y - 2 \sqrt{18 y}}}$

Step 1

Factor $2$ out of $50 y - 2 \sqrt{18 y}$ .

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Step 1.1

Factor $2$ out of $50 y$ .

$\sqrt{8 y + 5 \sqrt{2 (25 y) - 2 \sqrt{18 y}}}$

Step 1.2

Factor $2$ out of $- 2 \sqrt{18 y}$ .

$\sqrt{8 y + 5 \sqrt{2 (25 y) + 2 (- \sqrt{18 y})}}$

Step 1.3

Factor $2$ out of $2 (25 y) + 2 (- \sqrt{18 y})$ .

$\sqrt{8 y + 5 \sqrt{2 (25 y - \sqrt{18 y})}}$

Step 2

Apply basic rules of exponents.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{18 y}$ as ${(18 y)}^{\frac{1}{2}}$ .

$\sqrt{8 y + 5 \sqrt{2 (25 y - {(18 y)}^{\frac{1}{2}})}}$

Step 2.2

Apply the product rule to $18 y$ .

$\sqrt{8 y + 5 \sqrt{2 (25 y - (18^{\frac{1}{2}} y^{\frac{1}{2}}))}}$

Step 3

Factor $y^{\frac{1}{2}}$ out of $25 y - 18^{\frac{1}{2}} y^{\frac{1}{2}}$ .

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Step 3.1

Factor $y^{\frac{1}{2}}$ out of $25 y$ .

$\sqrt{8 y + 5 \sqrt{2 (y^{\frac{1}{2}} (25 y^{\frac{1}{2}}) - 18^{\frac{1}{2}} y^{\frac{1}{2}})}}$

Step 3.2

Factor $y^{\frac{1}{2}}$ out of $- 18^{\frac{1}{2}} y^{\frac{1}{2}}$ .

$\sqrt{8 y + 5 \sqrt{2 (y^{\frac{1}{2}} (25 y^{\frac{1}{2}}) + y^{\frac{1}{2}} (- 18^{\frac{1}{2}}))}}$

Step 3.3

Factor $y^{\frac{1}{2}}$ out of $y^{\frac{1}{2}} (25 y^{\frac{1}{2}}) + y^{\frac{1}{2}} (- 18^{\frac{1}{2}})$ .

$\sqrt{8 y + 5 \sqrt{2 (y^{\frac{1}{2}} (25 y^{\frac{1}{2}} - 18^{\frac{1}{2}}))}}$

$\sqrt{8 y + 5 \sqrt{2 y^{\frac{1}{2}} (25 y^{\frac{1}{2}} - 18^{\frac{1}{2}})}}$