Solve for h 0.9=2((2h)/32)^(1/2)

$0.9 = 2 {(\frac{2 h}{32})}^{\frac{1}{2}}$

Rewrite the equation as $2 {(\frac{2 h}{32})}^{\frac{1}{2}} = 0.9$ .

$2 {(\frac{2 h}{32})}^{\frac{1}{2}} = 0.9$

Reduce the expression $\frac{2 h}{32}$ by cancelling the common factors.

Factor $2$ out of $2 h$ .

$2 {(\frac{2 (h)}{32})}^{\frac{1}{2}} = 0.9$

Factor $2$ out of $32$ .

$2 {(\frac{2 h}{2 \cdot 16})}^{\frac{1}{2}} = 0.9$

Cancel the common factor.

$2 {(\frac{2 h}{2 \cdot 16})}^{\frac{1}{2}} = 0.9$

Rewrite the expression.

$2 {(\frac{h}{16})}^{\frac{1}{2}} = 0.9$

Divide each term in $2 {(\frac{h}{16})}^{\frac{1}{2}} = 0.9$ by $2$ and simplify.

Divide each term in $2 {(\frac{h}{16})}^{\frac{1}{2}} = 0.9$ by $2$ .

$\frac{2 {(\frac{h}{16})}^{\frac{1}{2}}}{2} = \frac{0.9}{2}$

Simplify the left side.

Reduce the expression by cancelling the common factors.

Cancel the common factor.

$\frac{2 {(\frac{h}{16})}^{\frac{1}{2}}}{2} = \frac{0.9}{2}$

Simplify the expression.

Divide ${(\frac{h}{16})}^{\frac{1}{2}}$ by $1$ .

${(\frac{h}{16})}^{\frac{1}{2}} = \frac{0.9}{2}$

Apply the product rule to $\frac{h}{16}$ .

$\frac{h^{\frac{1}{2}}}{16^{\frac{1}{2}}} = \frac{0.9}{2}$

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{h^{\frac{1}{2}}}{{(4^{2})}^{\frac{1}{2}}} = \frac{0.9}{2}$

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

$\frac{h^{\frac{1}{2}}}{4^{2 (\frac{1}{2})}} = \frac{0.9}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{h^{\frac{1}{2}}}{4^{2 (\frac{1}{2})}} = \frac{0.9}{2}$

Rewrite the expression.

$\frac{h^{\frac{1}{2}}}{4^{1}} = \frac{0.9}{2}$

Evaluate the exponent.

$\frac{h^{\frac{1}{2}}}{4} = \frac{0.9}{2}$

Simplify the right side.

Divide $0.9$ by $2$ .

$\frac{h^{\frac{1}{2}}}{4} = 0.45$

Multiply both sides of the equation by $4$ .

$4 \frac{h^{\frac{1}{2}}}{4} = 4 \cdot 0.45$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{h^{\frac{1}{2}}}{4} = 4 \cdot 0.45$

Rewrite the expression.

$h^{\frac{1}{2}} = 4 \cdot 0.45$

Simplify the right side.

Multiply $4$ by $0.45$ .

$h^{\frac{1}{2}} = 1.8$

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

${(h^{\frac{1}{2}})}^{2} = {1.8}^{2}$

Simplify the exponent.

Simplify the left side.

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

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

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

$h^{\frac{1}{2} \cdot 2} = {1.8}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$h^{\frac{1}{2} \cdot 2} = {1.8}^{2}$

Rewrite the expression.

$h^{1} = {1.8}^{2}$

Simplify.

$h = {1.8}^{2}$

Simplify the right side.

Raise $1.8$ to the power of $2$ .

$h = 3.24$

Solve for h 0.9=2((2h)/32)^(1/2)

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