Basic Math Examples

$\frac{\sqrt{s^{2} - 5 t}}{2} = 3$ us

Step 1

Multiply both sides by $2$ .

$\frac{\sqrt{s^{2} - 5 t}}{2} \cdot 2 = 3 \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{\sqrt{s^{2} - 5 t}}{2} \cdot 2 = 3 \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$\sqrt{s^{2} - 5 t} = 3 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $2$ .

$\sqrt{s^{2} - 5 t} = 6$

Step 3

Solve for $s$ .

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Step 3.1

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

${\sqrt{s^{2} - 5 t}}^{2} = 6^{2}$

Step 3.2

Simplify each side of the equation.

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Step 3.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{s^{2} - 5 t}$ as ${(s^{2} - 5 t)}^{\frac{1}{2}}$ .

${({(s^{2} - 5 t)}^{\frac{1}{2}})}^{2} = 6^{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Simplify ${({(s^{2} - 5 t)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.2.1.1

Multiply the exponents in ${({(s^{2} - 5 t)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.2.1.1.1

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

${(s^{2} - 5 t)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 3.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.2.1.1.2.1

Cancel the common factor.

${(s^{2} - 5 t)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 3.2.2.1.1.2.2

Rewrite the expression.

${(s^{2} - 5 t)}^{1} = 6^{2}$

Step 3.2.2.1.2

Simplify.

$s^{2} - 5 t = 6^{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

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

$s^{2} - 5 t = 36$

Step 3.3

Solve for $s$ .

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Step 3.3.1

Add $5 t$ to both sides of the equation.

$s^{2} = 36 + 5 t$

Step 3.3.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$s = \pm \sqrt{36 + 5 t}$

Step 3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$s = \sqrt{36 + 5 t}$

Step 3.3.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$s = - \sqrt{36 + 5 t}$

Step 3.3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$s = \sqrt{36 + 5 t}$

$s = - \sqrt{36 + 5 t}$

$s = \sqrt{36 + 5 t}$

$s = - \sqrt{36 + 5 t}$

$s = \sqrt{36 + 5 t}$

$s = - \sqrt{36 + 5 t}$

$s = \sqrt{36 + 5 t}$

$s = - \sqrt{36 + 5 t}$