Pre-Algebra Examples

$\sqrt{y^{5} - \sqrt{9 y^{5} - \sqrt{25 y}}}$

Step 1

Simplify the expression.

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{25 y}$ as ${(25 y)}^{\frac{1}{2}}$ .

$\sqrt{y^{5} - \sqrt{9 y^{5} - {(25 y)}^{\frac{1}{2}}}}$

Step 1.2

Apply the product rule to $25 y$ .

$\sqrt{y^{5} - \sqrt{9 y^{5} - (25^{\frac{1}{2}} y^{\frac{1}{2}})}}$

Step 1.3

Rewrite $25$ as $5^{2}$ .

$\sqrt{y^{5} - \sqrt{9 y^{5} - ({(5^{2})}^{\frac{1}{2}} y^{\frac{1}{2}})}}$

Step 1.4

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

$\sqrt{y^{5} - \sqrt{9 y^{5} - (5^{2 (\frac{1}{2})} y^{\frac{1}{2}})}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\sqrt{y^{5} - \sqrt{9 y^{5} - (5^{2 (\frac{1}{2})} y^{\frac{1}{2}})}}$

Step 2.2

Rewrite the expression.

$\sqrt{y^{5} - \sqrt{9 y^{5} - (5^{1} y^{\frac{1}{2}})}}$

Step 3

Evaluate the exponent.

$\sqrt{y^{5} - \sqrt{9 y^{5} - (5 y^{\frac{1}{2}})}}$

Step 4

Multiply $5$ by $- 1$ .

$\sqrt{y^{5} - \sqrt{9 y^{5} - 5 y^{\frac{1}{2}}}}$

Step 5

Factor $y^{\frac{1}{2}}$ out of $9 y^{5} - 5 y^{\frac{1}{2}}$ .

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Step 5.1

Factor $y^{\frac{1}{2}}$ out of $9 y^{5}$ .

$\sqrt{y^{5} - \sqrt{y^{\frac{1}{2}} (9 y^{\frac{9}{2}}) - 5 y^{\frac{1}{2}}}}$

Step 5.2

Factor $y^{\frac{1}{2}}$ out of $- 5 y^{\frac{1}{2}}$ .

$\sqrt{y^{5} - \sqrt{y^{\frac{1}{2}} (9 y^{\frac{9}{2}}) + y^{\frac{1}{2}} \cdot - 5}}$

Step 5.3

Factor $y^{\frac{1}{2}}$ out of $y^{\frac{1}{2}} (9 y^{\frac{9}{2}}) + y^{\frac{1}{2}} \cdot - 5$ .

$\sqrt{y^{5} - \sqrt{y^{\frac{1}{2}} (9 y^{\frac{9}{2}} - 5)}}$