Algebra Examples

$20 = \frac{5^{2} \sqrt{p}}{5}$

Step 1

Rewrite the equation as $\frac{5^{2} \sqrt{p}}{5} = 20$ .

$\frac{5^{2} \sqrt{p}}{5} = 20$

Step 2

Cancel the common factor of $5^{2}$ and $5$ .

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Step 2.1

Factor $5$ out of $5^{2} \sqrt{p}$ .

$\frac{5 (5 \sqrt{p})}{5} = 20$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $5$ .

$\frac{5 (5 \sqrt{p})}{5 (1)} = 20$

Step 2.2.2

Cancel the common factor.

$\frac{5 (5 \sqrt{p})}{5 \cdot 1} = 20$

Step 2.2.3

Rewrite the expression.

$\frac{5 \sqrt{p}}{1} = 20$

Step 2.2.4

Divide $5 \sqrt{p}$ by $1$ .

$5 \sqrt{p} = 20$

Step 3

Solve for $p$ .

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Step 3.1

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

${(5 \sqrt{p})}^{2} = 20^{2}$

Step 3.2

Simplify each side of the equation.

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Step 3.2.1

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

${(5 p^{\frac{1}{2}})}^{2} = 20^{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Simplify ${(5 p^{\frac{1}{2}})}^{2}$ .

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Step 3.2.2.1.1

Apply the product rule to $5 p^{\frac{1}{2}}$ .

$5^{2} {(p^{\frac{1}{2}})}^{2} = 20^{2}$

Step 3.2.2.1.2

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

$25 {(p^{\frac{1}{2}})}^{2} = 20^{2}$

Step 3.2.2.1.3

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

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Step 3.2.2.1.3.1

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

$25 p^{\frac{1}{2} \cdot 2} = 20^{2}$

Step 3.2.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.2.1.3.2.1

Cancel the common factor.

$25 p^{\frac{1}{2} \cdot 2} = 20^{2}$

Step 3.2.2.1.3.2.2

Rewrite the expression.

$25 p^{1} = 20^{2}$

Step 3.2.2.1.4

Simplify.

$25 p = 20^{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Raise $20$ to the power of $2$ .

$25 p = 400$

Step 3.3

Divide each term in $25 p = 400$ by $25$ and simplify.

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Step 3.3.1

Divide each term in $25 p = 400$ by $25$ .

$\frac{25 p}{25} = \frac{400}{25}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $25$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{25 p}{25} = \frac{400}{25}$

Step 3.3.2.1.2

Divide $p$ by $1$ .

$p = \frac{400}{25}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $400$ by $25$ .

$p = 16$