Precalculus Examples

\sqrt{s \sqrt{s^{3}}}

$\sqrt{s \sqrt{s^{3}}}$

Step 1

Factor out

s^{2}

$s^{2}$ .

\sqrt{s \sqrt{s^{2} s}}

$\sqrt{s \sqrt{s^{2} s}}$

Step 2

Pull terms out from under the radical.

\sqrt{s \cdot s \sqrt{s}}

$\sqrt{s \cdot s \sqrt{s}}$

Step 3

Combine exponents.

Tap for more steps...

Step 3.1

Raise

s

$s$ to the power of

1

$1$ .

\sqrt{s^{1} s \sqrt{s}}

$\sqrt{s^{1} s \sqrt{s}}$

Step 3.2

Raise

s

$s$ to the power of

1

$1$ .

\sqrt{s^{1} s^{1} \sqrt{s}}

$\sqrt{s^{1} s^{1} \sqrt{s}}$

Step 3.3

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\sqrt{s^{1 + 1} \sqrt{s}}

$\sqrt{s^{1 + 1} \sqrt{s}}$

Step 3.4

Add

1

$1$ and

1

$1$ .

\sqrt{s^{2} \sqrt{s}}

$\sqrt{s^{2} \sqrt{s}}$

$\sqrt{s^{2} \sqrt{s}}$

Step 4

Pull terms out from under the radical.

$s \sqrt{\sqrt{s}}$

Step 5

Rewrite

$\sqrt{\sqrt{s}}$ as

$\sqrt[4]{s}$ .

$s \sqrt[4]{s}$

$\sqrt[]{s \sqrt[]{s^{3}}}$

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥





















7

7

8

8

9

9













≤

≤





°

°

θ

θ









4

4

5

5

6

6

/

/

^

^

×

×

>

>





π

π













1

1

2

2

3

3

-

-

+

+

÷

÷

<

<





∞

∞











,

,

0

0

.

.

%

%



=

=









$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$