Algebra Examples

\sqrt{45} \cdot \sqrt{10}

$\sqrt{45} \cdot \sqrt{10}$

Step 1

Combine using the product rule for radicals.

\sqrt{45 \cdot 10}

$\sqrt{45 \cdot 10}$

Step 2

Multiply

45

$45$ by

10

$10$ .

\sqrt{450}

$\sqrt{450}$

Step 3

Rewrite

450

$450$ as

15^{2} \cdot 2

$15^{2} \cdot 2$ .

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Step 3.1

Factor

225

$225$ out of

450

$450$ .

\sqrt{225 (2)}

$\sqrt{225 (2)}$

Step 3.2

Rewrite

225

$225$ as

15^{2}

$15^{2}$ .

\sqrt{15^{2} \cdot 2}

$\sqrt{15^{2} \cdot 2}$

\sqrt{15^{2} \cdot 2}

$\sqrt{15^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

15 \sqrt{2}

$15 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

15 \sqrt{2}

$15 \sqrt{2}$

Decimal Form:

21.21320343 \dots

$21.21320343 \dots$

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

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