Solve by Factoring x^(1/2)=5

$x^{\frac{1}{2}} = 5$

Step 1

Subtract $5$ from both sides of the equation.

$x^{\frac{1}{2}} - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$x^{\frac{1}{2}} = 5$

Step 3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{2}})}^{2} = 5^{2}$

Step 4

Simplify the exponent.

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

$x^{1} = 5^{2}$

Simplify.

$x = 5^{2}$

Simplify the right side.

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

$x = 25$