Solve for k square root of k-4-1=5

$\sqrt{k - 4} - 1 = 5$

Step 1

Move all terms not containing $\sqrt{k - 4}$ to the right side of the equation.

Add $1$ to both sides of the equation.

$\sqrt{k - 4} = 5 + 1$

Add $5$ and $1$ .

$\sqrt{k - 4} = 6$

Step 2

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

${\sqrt{k - 4}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{k - 4}$ as ${(k - 4)}^{\frac{1}{2}}$ .

${({(k - 4)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(k - 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(k - 4)}^{\frac{1}{2}})}^{2}$ .

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

${(k - 4)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(k - 4)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(k - 4)}^{1} = 6^{2}$

Simplify.

$k - 4 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$k - 4 = 36$

Step 4

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

Add $4$ to both sides of the equation.

$k = 36 + 4$

Add $36$ and $4$ .

$k = 40$