Algebra Examples

$s = 20.05 \sqrt{t + 273.15}$

Step 1

Rewrite the equation as $20.05 \sqrt{t + 273.15} = s$ .

$20.05 \sqrt{t + 273.15} = s$

Step 2

Divide each term in $20.05 \sqrt{t + 273.15} = s$ by $20.05$ and simplify.

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Step 2.1

Divide each term in $20.05 \sqrt{t + 273.15} = s$ by $20.05$ .

$\frac{20.05 \sqrt{t + 273.15}}{20.05} = \frac{s}{20.05}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $20.05$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{20.05 \sqrt{t + 273.15}}{20.05} = \frac{s}{20.05}$

Step 2.2.1.2

Divide $\sqrt{t + 273.15}$ by $1$ .

$\sqrt{t + 273.15} = \frac{s}{20.05}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply by $1$ .

$\sqrt{t + 273.15} = \frac{1 s}{20.05}$

Step 2.3.2

Factor $20.05$ out of $20.05$ .

$\sqrt{t + 273.15} = \frac{1 s}{20.05 (1)}$

Step 2.3.3

Separate fractions.

$\sqrt{t + 273.15} = \frac{1}{20.05} \cdot \frac{s}{1}$

Step 2.3.4

Divide $1$ by $20.05$ .

$\sqrt{t + 273.15} = 0.04987531 \frac{s}{1}$

Step 2.3.5

Divide $s$ by $1$ .

$\sqrt{t + 273.15} = 0.04987531 s$

Step 3

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

${\sqrt{t + 273.15}}^{2} = {(0.04987531 s)}^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{t + 273.15}$ as ${(t + 273.15)}^{\frac{1}{2}}$ .

${({(t + 273.15)}^{\frac{1}{2}})}^{2} = {(0.04987531 s)}^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${({(t + 273.15)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Multiply the exponents in ${({(t + 273.15)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1.1

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

${(t + 273.15)}^{\frac{1}{2} \cdot 2} = {(0.04987531 s)}^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(t + 273.15)}^{\frac{1}{2} \cdot 2} = {(0.04987531 s)}^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(t + 273.15)}^{1} = {(0.04987531 s)}^{2}$

Step 4.2.1.2

Simplify.

$t + 273.15 = {(0.04987531 s)}^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify ${(0.04987531 s)}^{2}$ .

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Step 4.3.1.1

Apply the product rule to $0.04987531 s$ .

$t + 273.15 = {0.04987531}^{2} s^{2}$

Step 4.3.1.2

Raise $0.04987531$ to the power of $2$ .

$t + 273.15 = 0.00248754 s^{2}$

Step 5

Subtract $273.15$ from both sides of the equation.

$t = 0.00248754 s^{2} - 273.15$