Solve for x 6x^(1/2)=72

$6 x^{\frac{1}{2}} = 72$

Step 1

Divide each term in $6 x^{\frac{1}{2}} = 72$ by $6$ and simplify.

Divide each term in $6 x^{\frac{1}{2}} = 72$ by $6$ .

$\frac{6 x^{\frac{1}{2}}}{6} = \frac{72}{6}$

Simplify the left side.

Cancel the common factor.

$\frac{6 x^{\frac{1}{2}}}{6} = \frac{72}{6}$

Divide $x^{\frac{1}{2}}$ by $1$ .

$x^{\frac{1}{2}} = \frac{72}{6}$

Simplify the right side.

Divide $72$ by $6$ .

$x^{\frac{1}{2}} = 12$

Step 2

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

${(x^{\frac{1}{2}})}^{2} = 12^{2}$

Step 3

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, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$x^{1} = 12^{2}$

Simplify.

$x = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$x = 144$