Basic Math Examples

$\sqrt{5 y} \cdot \sqrt{10 y^{4}}$

Step 1

Rewrite $10 y^{4}$ as ${(y^{2})}^{2} \cdot 10$ .

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Step 1.1

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

$\sqrt{5 y} \cdot \sqrt{10 {(y^{2})}^{2}}$

Step 1.2

Reorder $10$ and ${(y^{2})}^{2}$ .

$\sqrt{5 y} \cdot \sqrt{{(y^{2})}^{2} \cdot 10}$

$\sqrt{5 y} \cdot \sqrt{{(y^{2})}^{2} \cdot 10}$

Step 2

Pull terms out from under the radical.

$\sqrt{5 y} \cdot (y^{2} \sqrt{10})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{10} \sqrt{5 y} y^{2}$

Step 4

Multiply $\sqrt{10} \sqrt{5 y}$ .

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Step 4.1

Combine using the product rule for radicals.

$\sqrt{10 (5 y)} y^{2}$

Step 4.2

Multiply $10$ by $5$ .

$\sqrt{50 y} y^{2}$

$\sqrt{50 y} y^{2}$

Step 5

Rewrite $50 y$ as $5^{2} \cdot (2 y)$ .

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Step 5.1

Factor $25$ out of $50$ .

$\sqrt{25 (2) y} y^{2}$

Step 5.2

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

$\sqrt{5^{2} \cdot 2 y} y^{2}$

Step 5.3

Add parentheses.

$\sqrt{5^{2} \cdot (2 y)} y^{2}$

$\sqrt{5^{2} \cdot (2 y)} y^{2}$

Step 6

Pull terms out from under the radical.

$5 \sqrt{2 y} y^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$