Finite Math Examples

$v = \sqrt{34 d}$

Step 1

Rewrite the equation as $\sqrt{34 d} = v$ .

$\sqrt{34 d} = v$

Step 2

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

${\sqrt{34 d}}^{2} = v^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{34 d}$ as ${(34 d)}^{\frac{1}{2}}$ .

${({(34 d)}^{\frac{1}{2}})}^{2} = v^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({(34 d)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in ${({(34 d)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1.1

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

${(34 d)}^{\frac{1}{2} \cdot 2} = v^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${(34 d)}^{\frac{1}{2} \cdot 2} = v^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(34 d)}^{1} = v^{2}$

Step 3.2.1.2

Simplify.

$34 d = v^{2}$

Step 4

Divide each term in $34 d = v^{2}$ by $34$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $34 d = v^{2}$ by $34$ .

$\frac{34 d}{34} = \frac{v^{2}}{34}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $34$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{34 d}{34} = \frac{v^{2}}{34}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{v^{2}}{34}$