Basic Math Examples

$(15 - y) \cdot \sqrt{11} = 3 \sqrt{44} + 8 \sqrt{99}$

Step 1

Simplify.

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Step 1.1

Rewrite $44$ as $2^{2} \cdot 11$ .

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Step 1.1.1

Factor $4$ out of $44$ .

$(15 - y) \cdot \sqrt{11} = 3 \sqrt{4 (11)} + 8 \sqrt{99}$

Step 1.1.2

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

$(15 - y) \cdot \sqrt{11} = 3 \sqrt{2^{2} \cdot 11} + 8 \sqrt{99}$

Step 1.2

Pull terms out from under the radical.

$(15 - y) \cdot \sqrt{11} = 3 (2 \sqrt{11}) + 8 \sqrt{99}$

Step 1.3

Multiply $2$ by $3$ .

$(15 - y) \cdot \sqrt{11} = 6 \sqrt{11} + 8 \sqrt{99}$

Step 1.4

Rewrite $99$ as $3^{2} \cdot 11$ .

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Step 1.4.1

Factor $9$ out of $99$ .

$(15 - y) \cdot \sqrt{11} = 6 \sqrt{11} + 8 \sqrt{9 (11)}$

Step 1.4.2

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

$(15 - y) \cdot \sqrt{11} = 6 \sqrt{11} + 8 \sqrt{3^{2} \cdot 11}$

Step 1.5

Pull terms out from under the radical.

$(15 - y) \cdot \sqrt{11} = 6 \sqrt{11} + 8 (3 \sqrt{11})$

Step 1.6

Multiply $3$ by $8$ .

$(15 - y) \cdot \sqrt{11} = 6 \sqrt{11} + 24 \sqrt{11}$

Step 1.7

Add $6 \sqrt{11}$ and $24 \sqrt{11}$ .

$(15 - y) \cdot \sqrt{11} = 30 \sqrt{11}$

Step 2

Divide each term in $(15 - y) \cdot \sqrt{11} = 30 \sqrt{11}$ by $\sqrt{11}$ and simplify.

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Step 2.1

Divide each term in $(15 - y) \cdot \sqrt{11} = 30 \sqrt{11}$ by $\sqrt{11}$ .

$\frac{(15 - y) \cdot \sqrt{11}}{\sqrt{11}} = \frac{30 \sqrt{11}}{\sqrt{11}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sqrt{11}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{(15 - y) \cdot \sqrt{11}}{\sqrt{11}} = \frac{30 \sqrt{11}}{\sqrt{11}}$

Step 2.2.1.2

Divide $15 - y$ by $1$ .

$15 - y = \frac{30 \sqrt{11}}{\sqrt{11}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $\sqrt{11}$ .

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Step 2.3.1.1

Cancel the common factor.

$15 - y = \frac{30 \sqrt{11}}{\sqrt{11}}$

Step 2.3.1.2

Divide $30$ by $1$ .

$15 - y = 30$

Step 3

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1

Subtract $15$ from both sides of the equation.

$- y = 30 - 15$

Step 3.2

Subtract $15$ from $30$ .

$- y = 15$

Step 4

Divide each term in $- y = 15$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- y = 15$ by $- 1$ .

$\frac{- y}{- 1} = \frac{15}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{15}{- 1}$

Step 4.2.2

Divide $y$ by $1$ .

$y = \frac{15}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $15$ by $- 1$ .

$y = - 15$