Solve for z 2(3z+4)^(1/2)=10

$2 {(3 z + 4)}^{\frac{1}{2}} = 10$

Divide each term in $2 {(3 z + 4)}^{\frac{1}{2}} = 10$ by $2$ and simplify.

Divide each term in $2 {(3 z + 4)}^{\frac{1}{2}} = 10$ by $2$ .

$\frac{2 {(3 z + 4)}^{\frac{1}{2}}}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor.

$\frac{2 {(3 z + 4)}^{\frac{1}{2}}}{2} = \frac{10}{2}$

Divide ${(3 z + 4)}^{\frac{1}{2}}$ by $1$ .

${(3 z + 4)}^{\frac{1}{2}} = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

${(3 z + 4)}^{\frac{1}{2}} = 5$

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

${({(3 z + 4)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(3 z + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 z + 4)}^{\frac{1}{2}})}^{2}$ .

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

${(3 z + 4)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 z + 4)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(3 z + 4)}^{1} = 5^{2}$

Simplify.

$3 z + 4 = 5^{2}$

Simplify the right side.

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

$3 z + 4 = 25$

Solve for $z$ .

Move all terms not containing $z$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$3 z = 25 - 4$

Subtract $4$ from $25$ .

$3 z = 21$

Divide each term in $3 z = 21$ by $3$ and simplify.

Divide each term in $3 z = 21$ by $3$ .

$\frac{3 z}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 z}{3} = \frac{21}{3}$

Divide $z$ by $1$ .

$z = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$z = 7$

Solve for z 2(3z+4)^(1/2)=10

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