Basic Math Examples

$\sqrt{f} + e = k$

Step 1

Subtract $e$ from both sides of the equation.

$\sqrt{f} = k - e$

Step 2

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

${\sqrt{f}}^{2} = {(k - e)}^{2}$

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 $\sqrt{f}$ as $f^{\frac{1}{2}}$ .

${(f^{\frac{1}{2}})}^{2} = {(k - e)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

$f^{\frac{1}{2} \cdot 2} = {(k - e)}^{2}$

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.

$f^{\frac{1}{2} \cdot 2} = {(k - e)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$f^{1} = {(k - e)}^{2}$

Step 3.2.1.2

Simplify.

$f = {(k - e)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(k - e)}^{2}$ .

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Step 3.3.1.1

Rewrite ${(k - e)}^{2}$ as $(k - e) (k - e)$ .

$f = (k - e) (k - e)$

Step 3.3.1.2

Expand $(k - e) (k - e)$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$f = k (k - e) - e (k - e)$

Step 3.3.1.2.2

Apply the distributive property.

$f = k \cdot k + k (- e) - e (k - e)$

Step 3.3.1.2.3

Apply the distributive property.

$f = k \cdot k + k (- e) - e k - e (- e)$

Step 3.3.1.3

Simplify and combine like terms.

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Step 3.3.1.3.1

Simplify each term.

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Step 3.3.1.3.1.1

Multiply $k$ by $k$ .

$f = k^{2} + k (- e) - e k - e (- e)$

Step 3.3.1.3.1.2

Multiply $- e (- e)$ .

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Step 3.3.1.3.1.2.1

Multiply $- 1$ by $- 1$ .

$f = k^{2} + k (- e) - e k + 1 e e$

Step 3.3.1.3.1.2.2

Multiply $e$ by $1$ .

$f = k^{2} + k (- e) - e k + e e$

Step 3.3.1.3.1.2.3

Raise $e$ to the power of $1$ .

$f = k^{2} + k (- e) - e k + e^{1} e$

Step 3.3.1.3.1.2.4

Raise $e$ to the power of $1$ .

$f = k^{2} + k (- e) - e k + e^{1} e^{1}$

Step 3.3.1.3.1.2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f = k^{2} + k (- e) - e k + e^{1 + 1}$

Step 3.3.1.3.1.2.6

Add $1$ and $1$ .

$f = k^{2} + k (- e) - e k + e^{2}$

Step 3.3.1.3.2

Move $e$ .

$f = k^{2} - 1 \cdot k e - 1 k e + e^{2}$

Step 3.3.1.3.3

Subtract $k e$ from $- 1 \cdot k e$ .

$f = k^{2} - 2 k e + e^{2}$