Name: Rationalizing a denominator: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 29 s
Description: Which of the following is equal to 10/√5? Try it, then watch the animated solution.

Picture

\tfrac{10}{\sqrt{5}}

as the width of a rectangle with area

10

and height

\sqrt{5}

.

A square of side

\sqrt{5}

has area

\sqrt{5} \times \sqrt{5} = 5

. Two such squares fill the area

10

.

In symbols, multiply top and bottom by

\sqrt{5}

. The bottom becomes

\sqrt{5} \times \sqrt{5} = 5

.

Divide:

\tfrac{10\sqrt{5}}{5} = 2\sqrt{5}

, matching the two squares in the picture.

Traps:

2

divides

10

by

5

and drops the root,

\sqrt{2}

is

\sqrt{10} \div \sqrt{5}

,

10\sqrt{5}

changes only the top.

Try it first