math !!B1

Question

change each mixed radicals or entire radicals to other form.

a) √32

b)2√6

c)√(9x³)

d) √(48xy²)

e) 9x²√(2x)

Answer 1

a) √32

Change the above entire radical to mixed radical.

32 is not perfect square.

Since we are trying to square root a number that isn't perfect square ,in order to simplify it we must use a perfect square to reduce it.

We break 32 down into the factors of 16 and 2.

= √(16*2)

= √(16)√(2)

= 4√(2)

√32 = 4√(2).

Answer 2

b) 2√6

Change the above mixed radical to entire radical.

Since there is a square root sign, the coefficient 2 must have come from square rooting a number.

2√6 = √4√6

{ Apply the radical property √a√b = √(ab)}

= √(4*6)

= √24

2√6 = √24 .

Answer 3

c)√(9x³)

Change the above entire radical to mixed radical.

9 is perfect square.

√(9x³) = √9√(x³)

= 3√(x³)

√(9x³) = 3√(x³).

We can able to write it √(9x³) = 3x√x.

Answer 4

d) √(48xy²)

Change the above entire radical to mixed radical.

48 is not perfect square.

We break 48 down into the factors of 16 and 3.

= √(16*3xy²)

= √(16*3x)√(y²)

= √(16)√(3x)√(y²)

= 4y√(3x)

√(48xy²) = 4y√(3x).

Answer 5

e) 9x²√(2x)

Change the above mixed radical to entire radical.

= √81x⁴√(2x)

{ Apply the radical property √a√b = √(ab)}

= √(81x⁴)(2x)

= √(81*2)(x⁴⁺¹)

= √(162x⁵)

9x²√(2x) = √(162x⁵).