Exercise 1 Page 270

To rationalize a fraction with a binomial denominator, we multiply the numerator and denominator of the fraction by the conjugate of the denominator. We find the conjugate by changing the sign of the second term of the expression.

Binomial	Conjugate
a + b	a - b
a - b	a + b

In this case, the conjugate of the denominator is 4-sqrt(2).

1/4+sqrt(2)

ExpandFrac

a/b=a * ( 4-sqrt(2))/b * ( 4-sqrt(2))

4-sqrt(2)/(4+sqrt(2))(4-sqrt(2))

ExpandDiffSquares

(a+b)(a-b)=a^2-b^2

4-sqrt(2)/4^2-(sqrt(2))^2

PowSqrt

( sqrt(a) )^2 = a

4-sqrt(2)/4^2-2

CalcPow

Calculate power

4-sqrt(2)/16-2

SubTerm

Subtract term

4-sqrt(2)/14

The rationalized expression equals 4-sqrt(2)14, which corresponds to answer H.