Solve for n square root of n-1=-7

$\sqrt{n - 1} = - 7$

Step 1

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

${\sqrt{n - 1}}^{2} = {(- 7)}^{2}$

Step 2

Simplify each side of the equation.

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

${({(n - 1)}^{\frac{1}{2}})}^{2} = {(- 7)}^{2}$

Simplify the left side.

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

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

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

${(n - 1)}^{\frac{1}{2} \cdot 2} = {(- 7)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(n - 1)}^{\frac{1}{2} \cdot 2} = {(- 7)}^{2}$

Rewrite the expression.

${(n - 1)}^{1} = {(- 7)}^{2}$

Simplify.

$n - 1 = {(- 7)}^{2}$

Simplify the right side.

Raise $- 7$ to the power of $2$ .

$n - 1 = 49$

Step 3

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

Add $1$ to both sides of the equation.

$n = 49 + 1$

Add $49$ and $1$ .

$n = 50$

Step 4

Exclude the solutions that do not make $\sqrt{n - 1} = - 7$ true.

$No solution$