Calculus Examples

$a \cdot 1 = \sqrt{5} + (n - 1) \sqrt{5}$

Step 1

Rewrite the equation as $\sqrt{5} + (n - 1) \sqrt{5} = a \cdot 1$ .

$\sqrt{5} + (n - 1) \sqrt{5} = a \cdot 1$

Step 2

Simplify $\sqrt{5} + (n - 1) \sqrt{5}$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$\sqrt{5} + n \sqrt{5} - 1 \sqrt{5} = a \cdot 1$

Step 2.1.2

Rewrite $- 1 \sqrt{5}$ as $- \sqrt{5}$ .

$\sqrt{5} + n \sqrt{5} - \sqrt{5} = a \cdot 1$

Step 2.2

Combine the opposite terms in $\sqrt{5} + n \sqrt{5} - \sqrt{5}$ .

Tap for more steps...

Step 2.2.1

Subtract $\sqrt{5}$ from $\sqrt{5}$ .

$n \sqrt{5} + 0 = a \cdot 1$

Step 2.2.2

Add $n \sqrt{5}$ and $0$ .

$n \sqrt{5} = a \cdot 1$

Step 3

Multiply $a$ by $1$ .

$n \sqrt{5} = a$

Step 4

Divide each term in $n \sqrt{5} = a$ by $\sqrt{5}$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $n \sqrt{5} = a$ by $\sqrt{5}$ .

$\frac{n \sqrt{5}}{\sqrt{5}} = \frac{a}{\sqrt{5}}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $\sqrt{5}$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{n \sqrt{5}}{\sqrt{5}} = \frac{a}{\sqrt{5}}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{a}{\sqrt{5}}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Multiply $\frac{a}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$n = \frac{a}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 4.3.2

Combine and simplify the denominator.

Tap for more steps...

Step 4.3.2.1

Multiply $\frac{a}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$n = \frac{a \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Step 4.3.2.2

Raise $\sqrt{5}$ to the power of $1$ .

$n = \frac{a \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Step 4.3.2.3

Raise $\sqrt{5}$ to the power of $1$ .

$n = \frac{a \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Step 4.3.2.4

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

$n = \frac{a \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Step 4.3.2.5

Add $1$ and $1$ .

$n = \frac{a \sqrt{5}}{{\sqrt{5}}^{2}}$

Step 4.3.2.6

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Tap for more steps...

Step 4.3.2.6.1

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

$n = \frac{a \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

Step 4.3.2.6.2

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

$n = \frac{a \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Step 4.3.2.6.3

Combine $\frac{1}{2}$ and $2$ .

$n = \frac{a \sqrt{5}}{5^{\frac{2}{2}}}$

Step 4.3.2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.3.2.6.4.1

Cancel the common factor.

$n = \frac{a \sqrt{5}}{5^{\frac{2}{2}}}$

Step 4.3.2.6.4.2

Rewrite the expression.

$n = \frac{a \sqrt{5}}{5^{1}}$

Step 4.3.2.6.5

Evaluate the exponent.

$n = \frac{a \sqrt{5}}{5}$