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Question

WRITE EACH OF THE FOLLOWING IN ENTIRE RADICALS AS A MIXED RADICALS IN SIMPLEST FORM.

1).  √72

2). √147

3). √175

4). ³√48

5). √54x²y³

6). ³√72xy^6

Answer 1

2)

RADICAL = √147

147 = 3*49

147 = 3*7²

√147 = √(3*7²)

Use formula : √(ab) = √(a)√(b)

= √(3)√(7²)

Use formula : √(a²) = a

= √(3)(7)

= 7√(3)

Simplified radical is 7√3

Answer 2

1)

RADICAL = √72

72 = 2*36

72 = 2*6²

√72 = √(2*6²)

Use formula : √(ab) = √(a)√(b)

= √(2)√(6²)

Use formula : √(a²) = a

= √(2)(6)

= 6√(2)

Simplified radical is 6√2

Answer 3

3)

RADICAL = √175

175 = 5*35

175 = 5*5*7

175 = 7*5²

√175 = √(7*5²)

Use formula : √(ab) = √(a)√(b)

= √(7)√(5²)

Use formula : √(a²) = a

= √(7)(5)

= 5√(7)

Simplified radical is 5√7

Answer 4

4)

RADICAL = ³√48

48 = 2*24

48 = 2*2*12

48 = 2*2*2*6

48 = 2³6

³√48 = ³√(2³6)

Use formula : √(ab) = √(a)√(b)

= ³√(2³)³√(6)

Use formula : ³√(a³) = a

= ³√(6)(2)

= 2(³√6)

Simplified radical is 2(³√6)

Answer 5

5)

RADICAL = √(54x²y³)

54 = 2*27

= 2*3*9

= 2*3*3²

= 6*3²

y³ = y*y*y = y²y

√(54x²y³) = √(6*3²*x²*y²*y)

= √[6y*(3xy)²]

Use formula : √(ab) = √(a)√(b)

= √[6y]√[(3xy)²]

Use formula : √(a²) = a

= √[6y][(3xy)]

= 3xy√(6y)

Simplified radical is 3xy√(6y).

Answer 6

6)

RADICAL = ³√72(xy⁶)

72 = 2*36

72 = 2*2*18

72 = 2*2*2*9

72 = 2³9

y⁶ = y*y*y*y*y*y

y⁶ = (y²)(y²)(y²)

y⁶ = (y²)³

³√72(xy⁶) = ³√[ (2³)(9)(x)(y²)³]

= ³√[ (2y²)³(9x)]

Use formula : √(ab) = √(a)√(b)

= ³√[(2y²)³] [³√(9x)]

Use formula : ³√(a³) = a

= (2y²)(³√(9x))

Simplified mixed radical is (2y²)[³√(9x)].