Solve by Factoring square root of 7x=35

$\sqrt{7 x} = 35$

Step 1

Subtract $35$ from both sides of the equation.

$\sqrt{7 x} - 35 = 0$

Step 2

Add $35$ to both sides of the equation.

$\sqrt{7 x} = 35$

Step 3

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

${\sqrt{7 x}}^{2} = 35^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

${({(7 x)}^{\frac{1}{2}})}^{2} = 35^{2}$

Simplify the left side.

Simplify ${({(7 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 x)}^{\frac{1}{2}})}^{2}$ .

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

${(7 x)}^{\frac{1}{2} \cdot 2} = 35^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 x)}^{\frac{1}{2} \cdot 2} = 35^{2}$

Rewrite the expression.

${(7 x)}^{1} = 35^{2}$

Simplify.

$7 x = 35^{2}$

Simplify the right side.

Raise $35$ to the power of $2$ .

$7 x = 1225$

Step 5

Divide each term in $7 x = 1225$ by $7$ and simplify.

Divide each term in $7 x = 1225$ by $7$ .

$\frac{7 x}{7} = \frac{1225}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{1225}{7}$

Divide $x$ by $1$ .

$x = \frac{1225}{7}$

Simplify the right side.

Divide $1225$ by $7$ .

$x = 175$