Basic Math Examples

3 \sqrt{k} = m

$3 \sqrt{k} = m$

Step 1

Divide each term in

3 \sqrt{k} = m

$3 \sqrt{k} = m$ by

3

$3$ and simplify.

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Step 1.1

Divide each term in

3 \sqrt{k} = m

$3 \sqrt{k} = m$ by

3

$3$ .

\frac{3 \sqrt{k}}{3} = \frac{m}{3}

$\frac{3 \sqrt{k}}{3} = \frac{m}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

3

$3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 \sqrt{k}}{3} = \frac{m}{3}$

Step 1.2.1.2

Divide

$\sqrt{k}$ by

$1$ .

$\sqrt{k} = \frac{m}{3}$

$\sqrt{k} = \frac{m}{3}$

$\sqrt{k} = \frac{m}{3}$

$\sqrt{k} = \frac{m}{3}$

Step 2

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

${\sqrt{k}}^{2} = {(\frac{m}{3})}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{k}$ as

$k^{\frac{1}{2}}$ .

${(k^{\frac{1}{2}})}^{2} = {(\frac{m}{3})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify

${(k^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in

${(k^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$k^{\frac{1}{2} \cdot 2} = {(\frac{m}{3})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of

$2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$k^{\frac{1}{2} \cdot 2} = {(\frac{m}{3})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$k^{1} = {(\frac{m}{3})}^{2}$

$k^{1} = {(\frac{m}{3})}^{2}$

$k^{1} = {(\frac{m}{3})}^{2}$

Step 3.2.1.2

Simplify.

$k = {(\frac{m}{3})}^{2}$

$k = {(\frac{m}{3})}^{2}$

$k = {(\frac{m}{3})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify

${(\frac{m}{3})}^{2}$ .

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Step 3.3.1.1

Apply the product rule to

$\frac{m}{3}$ .

$k = \frac{m^{2}}{3^{2}}$

Step 3.3.1.2

Raise

$3$ to the power of

$2$ .

$k = \frac{m^{2}}{9}$

$k = \frac{m^{2}}{9}$

$k = \frac{m^{2}}{9}$

$k = \frac{m^{2}}{9}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$