Enter the numerator and denominator.

RESULT

$\mathbf{\color{#3a5998}\dfrac{2\sqrt{72}}{\sqrt{5}}\color{black}=\color{chocolate}\dfrac{12\sqrt{10}}{5}}$

DESCRIPTIONS

Step 1 Find the Simplified Forms of the Numerator and Denominator

Numerator:
$2\sqrt{72}=2\sqrt{36.2}=$ $2.6\sqrt{2}=\mathbf{12\sqrt{2}}$
Denominator:
Denominator is in its simplest form.

We replace the numerator with its simplest form.

$\dfrac{2\sqrt{72}}{\sqrt{5}}=\mathbf{\dfrac{12\sqrt{2}}{\sqrt{5}}}$

Step 2 Simplify the Radicands

2 and 5 have no common factors greater than 1. Thus, the radicands cannot be simplifed.

Step 3 Rationalize the Denominator

To rationalize the denominator, we multiply both the numerator and denominator by $\sqrt{5}$ .

$\dfrac{12\sqrt{2}}{\sqrt{5}}=\dfrac{12\sqrt{2}.\sqrt{5}}{\sqrt{5}.\sqrt{5}}$ $=\mathbf{\dfrac{12\sqrt{10}}{5}}$

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INFORMATION

DIVISION OF SQUARE ROOTS

When dividing a square root by another, we can simplify the coefficients and radicands, separately. After those simplifications, we rationalize the denominator by multiplying both the numerator and denominator with the square root in the denominator. Finally, if it is possible we can simplify the coefficent of the numerator with the denominator.

WHAT IS SQUARE ROOT DIVISION CALCULATOR?

Square root division calculator,

Divides the entered square roots and
Describes all solution steps.

HOW TO USE SQUARE ROOT DIVISION CALCULATOR?

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

USER INPUTS

You can enter the coefficients and radicands to the input boxes and click on the "DIVIDE" 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 division 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.