Enter the factors. (Coefficients are optional.)

RESULT

$\mathbf{\color{#3a5998}3\color{black}\sqrt{\color{#3a5998}12}\color{black}\times\sqrt{\color{#3a5998}6}\color{black}=}$ $\mathbf{\color{chocolate}18\color{black}\sqrt{\color{chocolate}2}}$

DESCRIPTIONS

Step 1 Multiply the Coefficients

The coefficients of $\mathbf{\color{#3a5998}3\color{black}\sqrt{\color{#3a5998}12}}$ and $\mathbf{\sqrt{\color{#3a5998}6}}$ are $\mathbf{\color{#3a5998}3}$ and $\mathbf{\color{#3a5998}1}$ , respectively. The product of the coefficients is equal to $\mathbf{\color{olive}3}$ .

$\mathbf{\color{#3a5998}3\color{black}\sqrt{\color{#3a5998}12}\color{black}\times\sqrt{\color{#3a5998}6}\color{black}=}$ $\mathbf{\color{olive}3\color{black}(\sqrt{\color{#3a5998}12}\color{black}\times\sqrt{\color{#3a5998}6}\color{black})}$

Step 2 Multiply the Radicands

The product of 12 and 6 is equal to 72.

$\mathbf{\color{olive}3\color{black}(\sqrt{\color{#3a5998}12}\color{black}\times\sqrt{\color{#3a5998}6}\color{black})=}$ $\mathbf{\color{olive}3\color{black}\sqrt{\color{olive}72}}$

Step 3 Simplify the Expression

72 is equal to 36 × 2 where 36 is a perfect square.

$\mathbf{\color{olive}3\color{black}\sqrt{\color{olive}72}}$ $\mathbf{=\color{olive}3\color{black}\sqrt{36\times\color{chocolate}2}}$

36 can be taken out of the square root as $\mathbf{\sqrt{36}=6}$ .

$\mathbf{\color{olive}3\color{black}\sqrt{36\times\color{chocolate}2}}$ $\mathbf{=\color{olive}3\color{black}\times 6\sqrt{\color{chocolate}2}}$ $\mathbf{=\color{chocolate}18\color{black}\sqrt{\color{chocolate}2}}$

OTHER INFORMATION

👉 $\mathbf{\color{#3a5998}3\color{black}\sqrt{\color{#3a5998}12}\color{black}\times\sqrt{\color{#3a5998}6}\color{black}=}$ $\mathbf{\color{purple} 25.455844...}$

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INFORMATION

PRODUCT OF SQUARE ROOTS

So as to find the product of two square roots, we multiply the radicands and write the result inside a radical symbol.

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$

Provided that the radical expressions have coefficients, we write the product of these coefficients as the coefficient of the result.

$c\sqrt{a} \times d\sqrt{b} = c \times d\sqrt{a \times b}$

After the multiplication step, optionally we can simplify the resulting expression.

WHAT IS SQUARE ROOT MULTIPLICATION CALCULATOR?

Square root multiplication calculator,

Multiplies the entered square roots and
Describes all solution steps.

HOW TO USE SQUARE ROOT MULTIPLICATION CALCULATOR?

You can use the square root multiplication calculator in two ways.

USER INPUTS

You can enter the coefficients(optional) and radicands to the input boxes and click on the "MULTIPLY" button. The result and explanations appaer below the calculator
RANDOM INPUTS

You can click on the DIE ICON next to the input boxes. If you use this property, random numbers are generated and entered to the calculator, automatically. You can see the result and explanations below the calculator. You can create your own examples and practice using this property.
CLEARING THE INPUT BOX

To check the multiplication of other square roots you can clear the input boxes by clicking on the CLEAR button under the input boxes.
COPYING & DOWNLOADING THE SOLUTION
- You can copy the generated solution by clicking on the "Copy Text" link, appaers under the solution panel.
- Even you can download the solution as an image file with .jpg extension if you click on the "Download Solution" link at the bottom of the solution panel. You can share the downloaded image file.