Jay C.

asked • 06/03/17

# x=(√5−√7)^2, best approximation of x? Arithmetic

If x=(√5−√7)^2, what is the best approximation of x?

WHY is the answer is 0?? I got 4 by doing this:

x= (√5−√7)*(√5−√7); my answer after foiling was: x= 5-2-√35 + 7 = x= 10-√35...... so how does 2 attach (or 2 multiply ) the square root of 35? and why is it -(√35) instead of just -35? Christian S.

As noted in the answer below, you are using FOIL incorrectly.

(a-b)(a-b) = a2 - ab - ba + b2 = a2 - 2ab + b2
Report

06/04/17 Kris V.

Your approximation for x is 0 because
x = (√5 - √7)2 = 5 - 2√5√7 + 7 (as Mark indicated, and you know the equation (a - b)2 = a2 - 2ab + b2)
= 5 -2√(35) + 7
= 12 - 2√(35)
Since you were asked to estimate value of x, and 36 is a perfect square that is closet to 35
x ≅ 12 - 2√(36)
= 12 - 2(6)
= 0.
Report

06/04/17

## 1 Expert Answer

By: Mark M. answered • 06/03/17

Tutor
5.0 (243)

Mathematics Teacher - NCLB Highly Qualified

Jay C.

but when you foil its (√5−√7)*(√5−√7); so how does 5 - 2- √35 + 7 become 2√35??
Report

06/03/17 Mark M.

Multiplication rule of radicals
√a√b = √ab
√5√7 = √35
Report

06/03/17

Jay C.

but why isnt it 2- square root 35
Report

06/03/17 Mark M.

(a - b)2 = a2 - 2ab + b2  This is a general form that should be memorized
(√5 - √7)2
(√5)2 - 2√5√7 + (√7)2
Even if you use FOIL
(√5 - √7)(√5 - √7)
(√5)(√5) - √5√7 - √5√7 + (√7)(√7)
5 - 2√5√7 + 7
Report

06/03/17

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.
Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.