Pre-Algebra Examples

$\sqrt{7} (\sqrt{7} + y \sqrt{35})$

Step 1

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} (y \sqrt{35})$

Step 2

Combine using the product rule for radicals.

$\sqrt{7 \cdot 7} + \sqrt{7} (y \sqrt{35})$

Step 3

Multiply $\sqrt{7} (y \sqrt{35})$ .

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{7 \cdot 7} + y \sqrt{7 \cdot 35}$

Step 3.2

Multiply $7$ by $35$ .

$\sqrt{7 \cdot 7} + y \sqrt{245}$

$\sqrt{7 \cdot 7} + y \sqrt{245}$

Step 4

Simplify each term.

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Step 4.1

Multiply $7$ by $7$ .

$\sqrt{49} + y \sqrt{245}$

Step 4.2

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}} + y \sqrt{245}$

Step 4.3

Pull terms out from under the radical, assuming positive real numbers.

$7 + y \sqrt{245}$

Step 4.4

Rewrite $245$ as $7^{2} \cdot 5$ .

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Step 4.4.1

Factor $49$ out of $245$ .

$7 + y \sqrt{49 (5)}$

Step 4.4.2

Rewrite $49$ as $7^{2}$ .

$7 + y \sqrt{7^{2} \cdot 5}$

$7 + y \sqrt{7^{2} \cdot 5}$

Step 4.5

Pull terms out from under the radical.

$7 + y (7 \sqrt{5})$

Step 4.6

Move $7$ to the left of $y$ .

$7 + 7 y \sqrt{5}$

$7 + 7 y \sqrt{5}$

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