# Rationals and Radicals. 1) Solve for k:E=1-c/k 2)Simplify.(Rationalize the denominator if necessary) a.sqrt5/3x^2 b.4sqrtb/sqrt3-b?

1) Solve for k: E = 1 - c / k

2)Simplify. (Rationalize the denominator if necessary)

a. sqrt 5 / 3x^2

b. 4 sqrtb / sqrt3 - b <- (b is not in the sqrt with 3)

Relevance

1) E = 1 – (c / k) … assuming that’s what you mean

Multiplying both sides by k:

Ek = k – c

Subtract k from both sides:

Ek – k = -c

Factoring the LHS:

k(E – 1) = -c

k = -c / (E – 1)

2) (a) (√5) / (3x²) can’t be simplified any further but it can be written in different ways like:

Putting it all under the radical sign:

(√5) / (3x²) = (√5) / [√(9x⁴)] = √ [5 / (9x⁴)]

Or getting rid of the denominator:

(√5) / (3x²) = (√5) * 3⁻¹ x⁻² = 3⁻¹ x⁻² (√5)

But neither of those is simpler than the original

c) 4√b / [(√3) – b]

Rationalizing the denominator by multiplying numerator and denominator by [(√3) + b]:

= 4√b * [(√3) + b] / {[(√3) – b] * [(√3) + b]

= 4√b * [(√3) + b] / [3 - b²] … [and I’d leave it in that form b/c having a factored numerator is simpler than having it expanded]