Solve for R V = square root of (GM)/R

$V = \sqrt{\frac{G M}{R}}$

Step 1

Rewrite the equation as $\sqrt{\frac{G M}{R}} = V$ .

$\sqrt{\frac{G M}{R}} = V$

Step 2

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

${\sqrt{\frac{G M}{R}}}^{2} = V^{2}$

Step 3

Simplify each side of the equation.

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

${({(\frac{G M}{R})}^{\frac{1}{2}})}^{2} = V^{2}$

Simplify the left side.

Simplify ${({(\frac{G M}{R})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{G M}{R})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{G M}{R})}^{\frac{1}{2} \cdot 2} = V^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{G M}{R})}^{\frac{1}{2} \cdot 2} = V^{2}$

Rewrite the expression.

${(\frac{G M}{R})}^{1} = V^{2}$

Simplify.

$\frac{G M}{R} = V^{2}$

Step 4

Solve for $R$ .

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.

$R, 1$

The LCM of one and any expression is the expression.

$R$

Multiply each term in $\frac{G M}{R} = V^{2}$ by $R$ to eliminate the fractions.

Multiply each term in $\frac{G M}{R} = V^{2}$ by $R$ .

$\frac{G M}{R} R = V^{2} R$

Simplify the left side.

Cancel the common factor of $R$ .

Cancel the common factor.

$\frac{G M}{R} R = V^{2} R$

Rewrite the expression.

$G M = V^{2} R$

Solve the equation.

Rewrite the equation as $V^{2} R = G M$ .

$V^{2} R = G M$

Divide each term in $V^{2} R = G M$ by $V^{2}$ and simplify.

Divide each term in $V^{2} R = G M$ by $V^{2}$ .

$\frac{V^{2} R}{V^{2}} = \frac{G M}{V^{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{V^{2} R}{V^{2}} = \frac{G M}{V^{2}}$

Divide $R$ by $1$ .

$R = \frac{G M}{V^{2}}$

Solve for R V = square root of (GM)/R

Related Questions

Support LCMGCF.com by disabling your adblocker.