Pre-Algebra Examples

${(y + 5)}^{3} - 81 = 0$

Step 1

Add $81$ to both sides of the equation.

${(y + 5)}^{3} = 81$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y + 5 = \sqrt[3]{81}$

Step 3

Simplify $\sqrt[3]{81}$ .

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Step 3.1

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 3.1.1

Factor $27$ out of $81$ .

$y + 5 = \sqrt[3]{27 (3)}$

Step 3.1.2

Rewrite $27$ as $3^{3}$ .

$y + 5 = \sqrt[3]{3^{3} \cdot 3}$

Step 3.2

Pull terms out from under the radical.

$y + 5 = 3 \sqrt[3]{3}$

Step 4

Subtract $5$ from both sides of the equation.

$y = 3 \sqrt[3]{3} - 5$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = 3 \sqrt[3]{3} - 5$

Decimal Form:

$y = - 0.67325128 \dots$