Precalculus Examples

${(\frac{\sqrt{33} - 5}{4})}^{2}$

Step 1

Apply the product rule to $\frac{\sqrt{33} - 5}{4}$ .

$\frac{{(\sqrt{33} - 5)}^{2}}{4^{2}}$

Step 2

Raise $4$ to the power of $2$ .

$\frac{{(\sqrt{33} - 5)}^{2}}{16}$

Step 3

Simplify ${(\sqrt{33} - 5)}^{2}$ .

Tap for more steps...

Step 3.1

Rewrite ${(\sqrt{33} - 5)}^{2}$ as $(\sqrt{33} - 5) (\sqrt{33} - 5)$ .

$\frac{(\sqrt{33} - 5) (\sqrt{33} - 5)}{16}$

Step 3.2

Expand $(\sqrt{33} - 5) (\sqrt{33} - 5)$ using the FOIL Method.

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$\frac{\sqrt{33} (\sqrt{33} - 5) - 5 (\sqrt{33} - 5)}{16}$

Step 3.2.2

Apply the distributive property.

$\frac{\sqrt{33} \sqrt{33} + \sqrt{33} \cdot - 5 - 5 (\sqrt{33} - 5)}{16}$

Step 3.2.3

Apply the distributive property.

$\frac{\sqrt{33} \sqrt{33} + \sqrt{33} \cdot - 5 - 5 \sqrt{33} - 5 \cdot - 5}{16}$

Step 3.3

Simplify and combine like terms.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Combine using the product rule for radicals.

$\frac{\sqrt{33 \cdot 33} + \sqrt{33} \cdot - 5 - 5 \sqrt{33} - 5 \cdot - 5}{16}$

Step 3.3.1.2

Multiply $33$ by $33$ .

$\frac{\sqrt{1089} + \sqrt{33} \cdot - 5 - 5 \sqrt{33} - 5 \cdot - 5}{16}$

Step 3.3.1.3

Rewrite $1089$ as $33^{2}$ .

$\frac{\sqrt{33^{2}} + \sqrt{33} \cdot - 5 - 5 \sqrt{33} - 5 \cdot - 5}{16}$

Step 3.3.1.4

Pull terms out from under the radical, assuming positive real numbers.

$\frac{33 + \sqrt{33} \cdot - 5 - 5 \sqrt{33} - 5 \cdot - 5}{16}$

Step 3.3.1.5

Move $- 5$ to the left of $\sqrt{33}$ .

$\frac{33 - 5 \cdot \sqrt{33} - 5 \sqrt{33} - 5 \cdot - 5}{16}$

Step 3.3.1.6

Multiply $- 5$ by $- 5$ .

$\frac{33 - 5 \sqrt{33} - 5 \sqrt{33} + 25}{16}$

Step 3.3.2

Add $33$ and $25$ .

$\frac{58 - 5 \sqrt{33} - 5 \sqrt{33}}{16}$

Step 3.3.3

Subtract $5 \sqrt{33}$ from $- 5 \sqrt{33}$ .

$\frac{58 - 10 \sqrt{33}}{16}$

Step 4

Cancel the common factor of $58 - 10 \sqrt{33}$ and $16$ .

Tap for more steps...

Step 4.1

Factor $2$ out of $58$ .

$\frac{2 (29) - 10 \sqrt{33}}{16}$

Step 4.2

Factor $2$ out of $- 10 \sqrt{33}$ .

$\frac{2 (29) + 2 (- 5 \sqrt{33})}{16}$

Step 4.3

Factor $2$ out of $2 (29) + 2 (- 5 \sqrt{33})$ .

$\frac{2 (29 - 5 \sqrt{33})}{16}$

Step 4.4

Cancel the common factors.

Tap for more steps...

Step 4.4.1

Factor $2$ out of $16$ .

$\frac{2 (29 - 5 \sqrt{33})}{2 \cdot 8}$

Step 4.4.2

Cancel the common factor.

$\frac{2 (29 - 5 \sqrt{33})}{2 \cdot 8}$

Step 4.4.3

Rewrite the expression.

$\frac{29 - 5 \sqrt{33}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{29 - 5 \sqrt{33}}{8}$

Decimal Form:

$0.03464834 \dots$