Solve for x 3=(5^(1/2))(x^(1/2))

$3 = (5^{\frac{1}{2}}) (x^{\frac{1}{2}})$

Rewrite the equation as $5^{\frac{1}{2}} x^{\frac{1}{2}} = 3$ .

$5^{\frac{1}{2}} x^{\frac{1}{2}} = 3$

Divide each term in $5^{\frac{1}{2}} x^{\frac{1}{2}} = 3$ by $5^{\frac{1}{2}}$ and simplify.

Divide each term in $5^{\frac{1}{2}} x^{\frac{1}{2}} = 3$ by $5^{\frac{1}{2}}$ .

$\frac{5^{\frac{1}{2}} x^{\frac{1}{2}}}{5^{\frac{1}{2}}} = \frac{3}{5^{\frac{1}{2}}}$

Simplify the left side.

Cancel the common factor.

$\frac{5^{\frac{1}{2}} x^{\frac{1}{2}}}{5^{\frac{1}{2}}} = \frac{3}{5^{\frac{1}{2}}}$

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

$x^{\frac{1}{2}} = \frac{3}{5^{\frac{1}{2}}}$

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

${(x^{\frac{1}{2}})}^{2} = {(\frac{3}{5^{\frac{1}{2}}})}^{2}$

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

$x^{\frac{1}{2} \cdot 2} = {(\frac{3}{5^{\frac{1}{2}}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(\frac{3}{5^{\frac{1}{2}}})}^{2}$

Rewrite the expression.

$x^{1} = {(\frac{3}{5^{\frac{1}{2}}})}^{2}$

Simplify.

$x = {(\frac{3}{5^{\frac{1}{2}}})}^{2}$

Simplify the right side.

Simplify ${(\frac{3}{5^{\frac{1}{2}}})}^{2}$ .

Simplify the expression.

Apply the product rule to $\frac{3}{5^{\frac{1}{2}}}$ .

$x = \frac{3^{2}}{{(5^{\frac{1}{2}})}^{2}}$

Raise $3$ to the power of $2$ .

$x = \frac{9}{{(5^{\frac{1}{2}})}^{2}}$

Simplify the denominator.

Multiply the exponents in ${(5^{\frac{1}{2}})}^{2}$ .

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

$x = \frac{9}{5^{\frac{1}{2} \cdot 2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \frac{9}{5^{\frac{1}{2} \cdot 2}}$

Rewrite the expression.

$x = \frac{9}{5^{1}}$

Evaluate the exponent.

$x = \frac{9}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{5}$

Decimal Form:

$x = 1.8$

Mixed Number Form:

$x = 1 \frac{4}{5}$

Solve for x 3=(5^(1/2))(x^(1/2))

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