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math !!B1

0 votes

change each mixed radicals or entire radicals to other form.

a) √32

b)2√6

c)√(9x³)

d) √(48xy²)

e) 9x²√(2x)

asked Nov 21, 2014 in PRECALCULUS by anonymous

5 Answers

0 votes

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).

answered Nov 21, 2014 by david Expert
0 votes

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 = √46

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

= √(4*6)

= √24

2√6 = √24 .

answered Nov 21, 2014 by david Expert
0 votes

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.

answered Nov 21, 2014 by david Expert
edited Nov 21, 2014 by david
0 votes

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).

answered Nov 21, 2014 by david Expert
0 votes

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).

answered Nov 21, 2014 by david Expert

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