Basic Math Examples

$\sqrt{z + 20} = Z$

Step 1

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

${\sqrt{z + 20}}^{2} = Z^{2}$

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 $\sqrt{z + 20}$ as ${(z + 20)}^{\frac{1}{2}}$ .

${({(z + 20)}^{\frac{1}{2}})}^{2} = Z^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(z + 20)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(z + 20)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(z + 20)}^{\frac{1}{2} \cdot 2} = Z^{2}$

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.

${(z + 20)}^{\frac{1}{2} \cdot 2} = Z^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(z + 20)}^{1} = Z^{2}$

Step 2.2.1.2

Simplify.

$z + 20 = Z^{2}$

Step 3

Subtract $20$ from both sides of the equation.

$z = Z^{2} - 20$