Solve the Rational Equation for a 3 square root of 4a=42

$3 \sqrt{4 a} = 42$

To remove the radical on the left side of the equation, square both sides of the equation.

${(3 \sqrt{4 a})}^{2} = 42^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 a}$ as ${(4 a)}^{\frac{1}{2}}$ .

${(3 {(4 a)}^{\frac{1}{2}})}^{2} = 42^{2}$

Simplify the left side.

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

Simplify the expression.

Apply the product rule to $4 a$ .

${(3 (4^{\frac{1}{2}} a^{\frac{1}{2}}))}^{2} = 42^{2}$

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

${(3 ({(2^{2})}^{\frac{1}{2}} a^{\frac{1}{2}}))}^{2} = 42^{2}$

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

${(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Rewrite the expression.

${(3 (2^{1} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Evaluate the exponent.

${(3 (2 a^{\frac{1}{2}}))}^{2} = 42^{2}$

Multiply $2$ by $3$ .

${(6 a^{\frac{1}{2}})}^{2} = 42^{2}$

Apply the product rule to $6 a^{\frac{1}{2}}$ .

$6^{2} {(a^{\frac{1}{2}})}^{2} = 42^{2}$

Raise $6$ to the power of $2$ .

$36 {(a^{\frac{1}{2}})}^{2} = 42^{2}$

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

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

$36 a^{\frac{1}{2} \cdot 2} = 42^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$36 a^{\frac{1}{2} \cdot 2} = 42^{2}$

Rewrite the expression.

$36 a^{1} = 42^{2}$

Simplify.

$36 a = 42^{2}$

Simplify the right side.

Raise $42$ to the power of $2$ .

$36 a = 1764$

Divide each term in $36 a = 1764$ by $36$ and simplify.

Divide each term in $36 a = 1764$ by $36$ .

$\frac{36 a}{36} = \frac{1764}{36}$

Simplify the left side.

Cancel the common factor of $36$ .

Cancel the common factor.

$\frac{36 a}{36} = \frac{1764}{36}$

Divide $a$ by $1$ .

$a = \frac{1764}{36}$

Simplify the right side.

Divide $1764$ by $36$ .

$a = 49$

Solve the Rational Equation for a 3 square root of 4a=42

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