Solve for m 5 square root of m-1=40

$5 \sqrt{m - 1} = 40$

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

${(5 \sqrt{m - 1})}^{2} = 40^{2}$

Simplify each side of the equation.

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

${(5 {(m - 1)}^{\frac{1}{2}})}^{2} = 40^{2}$

Simplify the left side.

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

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

$5^{2} {({(m - 1)}^{\frac{1}{2}})}^{2} = 40^{2}$

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

$25 {({(m - 1)}^{\frac{1}{2}})}^{2} = 40^{2}$

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

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

$25 {(m - 1)}^{\frac{1}{2} \cdot 2} = 40^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 {(m - 1)}^{\frac{1}{2} \cdot 2} = 40^{2}$

Rewrite the expression.

$25 {(m - 1)}^{1} = 40^{2}$

Simplify.

$25 (m - 1) = 40^{2}$

Apply the distributive property.

$25 m + 25 \cdot - 1 = 40^{2}$

Multiply $25$ by $- 1$ .

$25 m - 25 = 40^{2}$

Simplify the right side.

Raise $40$ to the power of $2$ .

$25 m - 25 = 1600$

Solve for $m$ .

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

Add $25$ to both sides of the equation.

$25 m = 1600 + 25$

Add $1600$ and $25$ .

$25 m = 1625$

Divide each term in $25 m = 1625$ by $25$ and simplify.

Divide each term in $25 m = 1625$ by $25$ .

$\frac{25 m}{25} = \frac{1625}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 m}{25} = \frac{1625}{25}$

Divide $m$ by $1$ .

$m = \frac{1625}{25}$

Simplify the right side.

Divide $1625$ by $25$ .

$m = 65$

Solve for m 5 square root of m-1=40

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