Pre-Algebra Examples

$\sqrt{27 y} + \sqrt{12 y} + \sqrt{3 y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27 y$ as $3^{2} \cdot (3 y)$ .

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Step 1.1.1

Factor $9$ out of $27$ .

$\sqrt{9 (3) y} + \sqrt{12 y} + \sqrt{3 y}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 3 y} + \sqrt{12 y} + \sqrt{3 y}$

Step 1.1.3

Add parentheses.

$\sqrt{3^{2} \cdot (3 y)} + \sqrt{12 y} + \sqrt{3 y}$

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{3 y} + \sqrt{12 y} + \sqrt{3 y}$

Step 1.3

Rewrite $12 y$ as $2^{2} \cdot (3 y)$ .

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Step 1.3.1

Factor $4$ out of $12$ .

$3 \sqrt{3 y} + \sqrt{4 (3) y} + \sqrt{3 y}$

Step 1.3.2

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{3 y} + \sqrt{2^{2} \cdot 3 y} + \sqrt{3 y}$

Step 1.3.3

Add parentheses.

$3 \sqrt{3 y} + \sqrt{2^{2} \cdot (3 y)} + \sqrt{3 y}$

Step 1.4

Pull terms out from under the radical.

$3 \sqrt{3 y} + 2 \sqrt{3 y} + \sqrt{3 y}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 \sqrt{3 y}$ and $2 \sqrt{3 y}$ .

$5 \sqrt{3 y} + \sqrt{3 y}$

Step 2.2

Add $5 \sqrt{3 y}$ and $\sqrt{3 y}$ .

$6 \sqrt{3 y}$