Basic Math Examples

\sqrt{10 z} \cdot \sqrt{7 z}

$\sqrt{10 z} \cdot \sqrt{7 z}$

Step 1

Multiply

\sqrt{10 z} \sqrt{7 z}

$\sqrt{10 z} \sqrt{7 z}$ .

Tap for more steps...

Step 1.1

Combine using the product rule for radicals.

\sqrt{10 z (7 z)}

$\sqrt{10 z (7 z)}$

Step 1.2

Multiply

7

$7$ by

10

$10$ .

\sqrt{70 z \cdot z}

$\sqrt{70 z \cdot z}$

Step 1.3

Raise

z

$z$ to the power of

1

$1$ .

\sqrt{70 (z^{1} z)}

$\sqrt{70 (z^{1} z)}$

Step 1.4

Raise

z

$z$ to the power of

1

$1$ .

\sqrt{70 (z^{1} z^{1})}

$\sqrt{70 (z^{1} z^{1})}$

Step 1.5

Use the power rule

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

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

\sqrt{70 z^{1 + 1}}

$\sqrt{70 z^{1 + 1}}$

Step 1.6

Add

1

$1$ and

1

$1$ .

\sqrt{70 z^{2}}

$\sqrt{70 z^{2}}$

\sqrt{70 z^{2}}

$\sqrt{70 z^{2}}$

Step 2

Reorder

70

$70$ and

z^{2}

$z^{2}$ .

\sqrt{z^{2} \cdot 70}

$\sqrt{z^{2} \cdot 70}$

Step 3

Pull terms out from under the radical.

z \sqrt{70}

$z \sqrt{70}$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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