Algebra Examples

$\sqrt{x + 60} = \sqrt{x + 6}$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x + 60}}^{2} = {\sqrt{x + 6}}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 60}$ as ${(x + 60)}^{\frac{1}{2}}$ .

${({(x + 60)}^{\frac{1}{2}})}^{2} = {\sqrt{x + 6}}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(x + 60)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(x + 60)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 60)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 6}}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(x + 60)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 6}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(x + 60)}^{1} = {\sqrt{x + 6}}^{2}$

Step 2.2.1.2

Simplify.

$x + 60 = {\sqrt{x + 6}}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Rewrite ${\sqrt{x + 6}}^{2}$ as $x + 6$ .

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Step 2.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 6}$ as ${(x + 6)}^{\frac{1}{2}}$ .

$x + 60 = {({(x + 6)}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x + 60 = {(x + 6)}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.3

Combine $\frac{1}{2}$ and $2$ .

$x + 60 = {(x + 6)}^{\frac{2}{2}}$

Step 2.3.1.4

Cancel the common factor of $2$ .

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Step 2.3.1.4.1

Cancel the common factor.

$x + 60 = {(x + 6)}^{\frac{2}{2}}$

Step 2.3.1.4.2

Rewrite the expression.

$x + 60 = {(x + 6)}^{1}$

Step 2.3.1.5

Simplify.

$x + 60 = x + 6$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$x + 60 - x = 6$

Step 3.1.2

Combine the opposite terms in $x + 60 - x$ .

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Step 3.1.2.1

Subtract $x$ from $x$ .

$0 + 60 = 6$

Step 3.1.2.2

Add $0$ and $60$ .

$60 = 6$

Step 3.2

Since $60 \neq 6$ , there are no solutions.

No solution