Solve for n 4 square root of 5n-20=16

$4 \sqrt{5 n - 20} = 16$

Step 1

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

${(4 \sqrt{5 n - 20})}^{2} = 16^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 n - 20}$ as ${(5 n - 20)}^{\frac{1}{2}}$ .

${(4 {(5 n - 20)}^{\frac{1}{2}})}^{2} = 16^{2}$

Simplify the left side.

Simplify ${(4 {(5 n - 20)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $4 {(5 n - 20)}^{\frac{1}{2}}$ .

$4^{2} {({(5 n - 20)}^{\frac{1}{2}})}^{2} = 16^{2}$

Raise $4$ to the power of $2$ .

$16 {({(5 n - 20)}^{\frac{1}{2}})}^{2} = 16^{2}$

Multiply the exponents in ${({(5 n - 20)}^{\frac{1}{2}})}^{2}$ .

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

$16 {(5 n - 20)}^{\frac{1}{2} \cdot 2} = 16^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(5 n - 20)}^{\frac{1}{2} \cdot 2} = 16^{2}$

Rewrite the expression.

$16 {(5 n - 20)}^{1} = 16^{2}$

Simplify.

$16 (5 n - 20) = 16^{2}$

Apply the distributive property.

$16 (5 n) + 16 \cdot - 20 = 16^{2}$

Multiply.

Multiply $5$ by $16$ .

$80 n + 16 \cdot - 20 = 16^{2}$

Multiply $16$ by $- 20$ .

$80 n - 320 = 16^{2}$

Simplify the right side.

Raise $16$ to the power of $2$ .

$80 n - 320 = 256$

Step 3

Solve for $n$ .

Move all terms not containing $n$ to the right side of the equation.

Add $320$ to both sides of the equation.

$80 n = 256 + 320$

Add $256$ and $320$ .

$80 n = 576$

Divide each term in $80 n = 576$ by $80$ and simplify.

Divide each term in $80 n = 576$ by $80$ .

$\frac{80 n}{80} = \frac{576}{80}$

Simplify the left side.

Cancel the common factor of $80$ .

Cancel the common factor.

$\frac{80 n}{80} = \frac{576}{80}$

Divide $n$ by $1$ .

$n = \frac{576}{80}$

Simplify the right side.

Cancel the common factor of $576$ and $80$ .

Factor $16$ out of $576$ .

$n = \frac{16 (36)}{80}$

Cancel the common factors.

Factor $16$ out of $80$ .

$n = \frac{16 \cdot 36}{16 \cdot 5}$

Cancel the common factor.

$n = \frac{16 \cdot 36}{16 \cdot 5}$

Rewrite the expression.

$n = \frac{36}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{36}{5}$

Decimal Form:

$n = 7.2$

Mixed Number Form:

$n = 7 \frac{1}{5}$

Solve for n 4 square root of 5n-20=16

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