Finite Math Examples

$\sqrt{\sqrt{243 (x + 1)}}$

Step 1

Rewrite $243 (x + 1)$ as ${(3^{2})}^{2} \cdot (3 (x + 1))$ .

Tap for more steps...

Step 1.1

Factor $81$ out of $243$ .

$\sqrt{\sqrt{81 (3) (x + 1)}}$

Step 1.2

Rewrite $81$ as $9^{2}$ .

$\sqrt{\sqrt{9^{2} \cdot 3 (x + 1)}}$

Step 1.3

Rewrite $9$ as $3^{2}$ .

$\sqrt{\sqrt{{(3^{2})}^{2} \cdot 3 (x + 1)}}$

Step 1.4

Add parentheses.

$\sqrt{\sqrt{{(3^{2})}^{2} \cdot (3 (x + 1))}}$

Step 2

Pull terms out from under the radical.

$\sqrt{3^{2} \sqrt{3 (x + 1)}}$

Step 3

Raise $3$ to the power of $2$ .

$\sqrt{9 \sqrt{3 (x + 1)}}$

Step 4

Rewrite $9 \sqrt{3 (x + 1)}$ as $3^{2} \sqrt{3 (x + 1^{2})}$ .

Tap for more steps...

Step 4.1

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \sqrt{3 (x + 1)}}$

Step 4.2

Rewrite $1$ as $1^{2}$ .

$\sqrt{3^{2} \sqrt{3 (x + 1^{2})}}$

Step 5

Pull terms out from under the radical.

$3 \sqrt{\sqrt{3 (x + 1^{2})}}$

Step 6

One to any power is one.

$3 \sqrt{\sqrt{3 (x + 1)}}$

Step 7

Rewrite $\sqrt{\sqrt{3 (x + 1)}}$ as $\sqrt[4]{3 (x + 1)}$ .

$3 \sqrt[4]{3 (x + 1)}$