Algebra Examples

$(8 - 9 \sqrt[4]{36}) (5 + 4 \sqrt[4]{27})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $36$ as $6^{2}$ .

$(8 - 9 \sqrt[4]{6^{2}}) (5 + 4 \sqrt[4]{27})$

Step 1.2

Rewrite $\sqrt[4]{6^{2}}$ as $\sqrt{\sqrt{6^{2}}}$ .

$(8 - 9 \sqrt{\sqrt{6^{2}}}) (5 + 4 \sqrt[4]{27})$

Step 1.3

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

$(8 - 9 \sqrt{6}) (5 + 4 \sqrt[4]{27})$

Step 2

Expand $(8 - 9 \sqrt{6}) (5 + 4 \sqrt[4]{27})$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$8 (5 + 4 \sqrt[4]{27}) - 9 \sqrt{6} (5 + 4 \sqrt[4]{27})$

Step 2.2

Apply the distributive property.

$8 \cdot 5 + 8 (4 \sqrt[4]{27}) - 9 \sqrt{6} (5 + 4 \sqrt[4]{27})$

Step 2.3

Apply the distributive property.

$8 \cdot 5 + 8 (4 \sqrt[4]{27}) - 9 \sqrt{6} \cdot 5 - 9 \sqrt{6} (4 \sqrt[4]{27})$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $8$ by $5$ .

$40 + 8 (4 \sqrt[4]{27}) - 9 \sqrt{6} \cdot 5 - 9 \sqrt{6} (4 \sqrt[4]{27})$

Step 3.2

Multiply $4$ by $8$ .

$40 + 32 \sqrt[4]{27} - 9 \sqrt{6} \cdot 5 - 9 \sqrt{6} (4 \sqrt[4]{27})$

Step 3.3

Multiply $5$ by $- 9$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 9 \sqrt{6} (4 \sqrt[4]{27})$

Step 3.4

Multiply $- 9 \sqrt{6} (4 \sqrt[4]{27})$ .

Tap for more steps...

Step 3.4.1

Multiply $4$ by $- 9$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 \sqrt{6} \sqrt[4]{27}$

Step 3.4.2

Rewrite the expression using the least common index of $4$ .

Tap for more steps...

Step 3.4.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 (\sqrt[4]{27} \cdot 6^{\frac{1}{2}})$

Step 3.4.2.2

Rewrite $6^{\frac{1}{2}}$ as $6^{\frac{2}{4}}$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 (\sqrt[4]{27} \cdot 6^{\frac{2}{4}})$

Step 3.4.2.3

Rewrite $6^{\frac{2}{4}}$ as $\sqrt[4]{6^{2}}$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 (\sqrt[4]{27} \sqrt[4]{6^{2}})$

Step 3.4.3

Combine using the product rule for radicals.

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 \sqrt[4]{27 \cdot 6^{2}}$

Step 3.4.4

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

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 \sqrt[4]{27 \cdot 36}$

Step 3.4.5

Multiply $27$ by $36$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 \sqrt[4]{972}$

Step 3.5

Rewrite $972$ as $3^{4} \cdot 12$ .

Tap for more steps...

Step 3.5.1

Factor $81$ out of $972$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 \sqrt[4]{81 (12)}$

Step 3.5.2

Rewrite $81$ as $3^{4}$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 \sqrt[4]{3^{4} \cdot 12}$

Step 3.6

Pull terms out from under the radical.

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 36 (3 \sqrt[4]{12})$

Step 3.7

Multiply $3$ by $- 36$ .

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 108 \sqrt[4]{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$40 + 32 \sqrt[4]{27} - 45 \sqrt{6} - 108 \sqrt[4]{12}$

Decimal Form:

$- 198.29346216 \dots$