# Verify that rationalizing the denominator and squaring both numerator and denominator are same.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.4, Problem 104E
To determine

## Verify that rationalizing the denominator and squaring both numerator and denominator are same.

Expert Solution

No, its not the same thing.

### Explanation of Solution

Calculation:

Here, we have:

2x

Now, we will eliminate the radical by squaring it:

(2x)2=22(x)2=4x

Now, when we rationalize the denominator we get:

2x=2x×xx2x=2x(x)22x=2xx

Thus, the elimination of the radical by rationalize the denominator is 2x=2xx

Hence, the elimination of the radical by squaring both numerator and denominator is not the same thing as rationalizing the denominator.

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