In the following exercises, simplify.

72-6

Short Answer

Expert verified

Simplifying,

72-6=-14+762

Step by step solution

01

Step 1. Given information

We have given,

72-6

02

Step 2. Concept

To rationalize the denominator we need to multiply numerator and denominator by a conjugate of the denominator.

Then we will use the difference of two squares formula and distributive property to simplify it ahead,

Distributive property,

a(b + c) = ab + ac.

Difference of two squares formula,

a-ba+b=a2-b2

03

Step 3. Explanation

We have,

72-6

Multiplying numerator and denominator by conjugate of 2-6,

72+62-62+6

Using difference of two squares formula and distributive property,

14+7622-62

14+76-2

04

Step 4. Conclusion

Hence, rationalizing and simplifying 72-6we will get,-14+762.

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