pre calculus help.

Question

simplify the expression below by simplifying the radicals and collecting like terms.

a)  7√(50x) + 9√(75x³) - 2√(147x³) + √(32x)

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b) Show how to determine whether 7√5 or 9√3 is larger without using decimal values.

Answer 1

a)

The radical expression is 7√(50x) + 9√(75x³ ) - 2√(147x³) + √(32x)

= 7√(25*2x) + 9√(25*3x³) - 2√(49*3x³) + √(16*2x)

{Apply the radical property √(ab) = √a √b where a ≥ 0 and b ≥ 0}

= 7[√25√(2x)] + 9[√25√(3x³)] - 2[√49√(3x³)] + √16√(2x)

= 7[5√(2x)] + 9[5√(3x³)] - 2[7√(3x³)] + 4√(2x)

= 35√(2x) + 45√(3x³)] - 14√(3x³) + 4√(2x)

= 39√(2x) + 31√(3x³)

7√(50x) + 9√(75x³ ) - 2√(147x³) + √(32x) = 39√(2x) + 31√(3x³).

Answer 2

b)

The radicals are 7√5 and 9√3

Now determine which is larger

{Apply the radical property √(a²) = a where a ≥ 0}

7√5  = √(7²*5)

= √(49*5)

= √(245)

9√3 = √(9²*3)

= √(81*3) 

= √(243)

So 7√5 = √(245) and 9√3 = √(243)

243 < 245

7√5 is larger than 9√3.