Solve for a t = square root of (4p^2R)/a

$t = \sqrt{\frac{4 p^{2} R}{a}}$

Step 1

Rewrite the equation as $\sqrt{\frac{4 p^{2} R}{a}} = t$ .

$\sqrt{\frac{4 p^{2} R}{a}} = t$

Step 2

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

${\sqrt{\frac{4 p^{2} R}{a}}}^{2} = t^{2}$

Step 3

Simplify each side of the equation.

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

${({(\frac{4 p^{2} R}{a})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

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

Multiply the exponents in ${({(\frac{4 p^{2} R}{a})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{4 p^{2} R}{a})}^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{4 p^{2} R}{a})}^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

${(\frac{4 p^{2} R}{a})}^{1} = t^{2}$

Simplify.

$\frac{4 p^{2} R}{a} = t^{2}$

Step 4

Solve for $a$ .

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a, 1$

The LCM of one and any expression is the expression.

$a$

Multiply each term in $\frac{4 p^{2} R}{a} = t^{2}$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{4 p^{2} R}{a} = t^{2}$ by $a$ .

$\frac{4 p^{2} R}{a} a = t^{2} a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{4 p^{2} R}{a} a = t^{2} a$

Rewrite the expression.

$4 p^{2} R = t^{2} a$

Solve the equation.

Rewrite the equation as $t^{2} a = 4 p^{2} R$ .

$t^{2} a = 4 p^{2} R$

Divide each term in $t^{2} a = 4 p^{2} R$ by $t^{2}$ and simplify.

Divide each term in $t^{2} a = 4 p^{2} R$ by $t^{2}$ .

$\frac{t^{2} a}{t^{2}} = \frac{4 p^{2} R}{t^{2}}$

Simplify the left side.

Cancel the common factor of $t^{2}$ .

Cancel the common factor.

$\frac{t^{2} a}{t^{2}} = \frac{4 p^{2} R}{t^{2}}$

Divide $a$ by $1$ .

$a = \frac{4 p^{2} R}{t^{2}}$

Solve for a t = square root of (4p^2R)/a

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