Calculus Examples

$\sqrt{x} + 3 = 8$

Step 1

Move all terms not containing $\sqrt{x}$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$\sqrt{x} = 8 - 3$

Step 1.2

Subtract $3$ from $8$ .

$\sqrt{x} = 5$

Step 2

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

${\sqrt{x}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

${(x^{\frac{1}{2}})}^{2} = 5^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$x^{1} = 5^{2}$

Step 3.2.1.2

Simplify.

$x = 5^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $5$ to the power of $2$ .

$x = 25$

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