Solve for p 20=(5^2 square root of p)/5

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

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

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

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

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

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

Cancel the common factors.

Factor $5$ out of $5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$5 \sqrt{p} = 20$

Solve for $p$ .

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$25 p = 20^{2}$

Simplify the right side.

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

$25 p = 400$

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

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

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

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

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

Divide $p$ by $1$ .

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

Simplify the right side.

Divide $400$ by $25$ .

$p = 16$

Solve for p 20=(5^2 square root of p)/5

Related Questions

Support LCMGCF.com by disabling your adblocker.