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
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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.
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06/04/17

1 Expert Answer

By:

Mark M. answered • 06/03/17

Tutor
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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??
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06/03/17

Mark M.

Multiplication rule of radicals
√a√b = √ab
√5√7 = √35
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06/03/17

Jay C.

but why isnt it 2- square root 35
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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
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06/03/17

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