Download 20) Simplify by factoring. Assume that all expressions

20) Simplify by factoring. Assume that all expressions under the radical represent
nonnegative numbers. ?(324x^12y^14 ) = (Type an exact answer, using radicals as
needed)
324 x12 y14 = 18x 6 y 7
! 21) Simplify by factoring. Assume that all expressions under the radical represent
nonnegative numbers. v(5&64x^12y^15 ) = (Simplify your answer. Type in radical form)
5
64 x12 y15 = 2x 2 y 3 5 2x 2
! 23) Multiply and Simplify by factoring. Assume that all expressions under the radical
represent nonnegative numbers. v(5b^7) v(10c^8 ) = (Simplify your answer. Type in
radical form)
5b 7 10c 8 = 50b 7c 8 = 5b 3c 4 2b
! 27) Simplify by taking roots of the numerator and the denominator. Assume that all
expressions under radical represent positive numbers. v(5&(32x^13)/y^20 ) =
5
32x13 2x 2 5 3
= 4 x
y 20
y
! 29) Add. Simplify by collecting like radical terms if possible. 5v(75 )+ 3v108 = (Type an
exact answer, using radicals as needed)
5 75 + 3 108 = 25 3 +18 3 = 43 5
!
30) Add. Simplify by collecting like radical terms if possible, assume that all expressions
under the radical represent nonnegative numbers. v(7a ) + 9v(28a^3 ) = (Type an exact
answer, using radicals as needed)
7a + 9 28a 3 = 7a +18a 7a = (1+18a) 7a
! 31) Multiply v2 (6 -8)v(2 )) = (Simplify your answer. Type an exact answer, using
radicals as needed)
(
)
2 6 " 8 2 = 6 2 "16
! 32) Multiply ?a (?(5a^2 ) +?(625a^2 )) = (Simplify your answer. Type an exact answer,
using radicals as needed)
3
a
(
3
)
5a 2 + 3 625a 2 = 3 5a 3 + 3 625a 3 = a 3 5 + 5a 3 5 = 6a" 3 5
! 33) Multiply (7+v10)(7 -v10) = (Simplify your answer. Type an exact answer, using
radicals as needed)
(7 +
)(
)
10 7 " 10 = 49 "10 = 39
! 34) Multiply (v(5&4) - v(5&2))(v(5&125) +v(5&8)) =
(
5
4 "5 2
)(
5
)
125 " 5 8 = 5 500 " 5 250 " 5 32 + 5 16 = 5 500 " 5 250 " 2 + 5 16
! 17) Simplify by factoring?405. The answer is = (Type an exact answer, using radicals as
needed)
405 = 9 5
!
19) Multiply and Simplify by factoring. Assume that all expressions under the radical
represent nonnegative numbers. ?(y^13 ) ?(16y^14 ) = (Simplify your answer. Type in
radical form)
y13 3 16y14 = 3 16y 27 = 2y 9 3 2
3
! 20) Simplify by factoring. Assume that all expressions under the radical represent
nonnegative numbers. ?(810x^12y14) = (Type an exact answer, using radicals as needed)
4
810x12 y14 = 3x 3 y 3 4 10y 2
or
!
810x12 y14 = 9x 6 y 7 10
! 21) Simplify by factoring. Assume that all expressions under the radical represent
nonnegative numbers. v(5&320x^12y^15) = (Type an exact answer, using radicals as
needed)
5
320x12 y15 = 2x 2 y 3 5 10x 2
! 22) Multiply and Simplify by factoring. v8 * v150 Answer is __. (Type an exact answer,
using radicals as needed)
8 150 = 20 3
! 23) Multiply and Simplify by factoring. Assume that all expressions under the radical
represent nonnegative numbers. v(3b^5 ) v(33c^6 )
3b 5 33c 6 = 99b 5c 6 = 3b 2c 3 11b
!
25) Divide. Then simplify by taking roots, if possible. Assume that all expressions under
radical represent positive numbers. ?(162a^7 b^2 )/?(6a^5 b^1 ) = ___.
162a 7b 2
6a 5b
=
162a 7b 2
= 27a 2b = 3a 3b
6a 5b
! 27) Simplify by taking roots of the numerator and the denominator. Assume that all
expressions under radical represent positive numbers. v(5&(243x^18)/y^10 ) =
5
243x18 3x 3 5 3
= 2 x
y10
y
! 29) Add. Simplify by collecting like radical terms if possible. 4v27 + 8v75 = (Simplify
your answer. Type an exact answer, using radicals as needed)
4 27 + 8 75 = 12 3 + 40 3 = 52 3
! 30) Add. Simplify by collecting like radical terms if possible, assume that all expressions
under the radical represent nonnegative numbers. v5a + 7v(?20?^3 ) = (Simplify your
answer. Type an exact answer, using radicals as needed)
5a + 7 20a 3 = 5a +14a 20a = (1+14a) 5a
! 31) Multiply v(10 ) (6- 5v10) = (Simplify your answer. Type an exact answer, using
radicals as needed)
(
)
10 6 " 5 10 = 6 10 " 50
! 32) Multiply ?(a )(?(2a^2 ) + ?(16a^2 ) = (Simplify your answer. Type an exact answer,
using radicals as needed)
3
!
a
(
3
)
2a 2 + 3 16a 2 = 3 2a 3 + 3 16a 3 = a 3 2 + 2a 3 2 = 3a 3 2
33) Multiply (8+ v5)(8 - v5) = (Simplify your answer. Type an exact answer, using
radicals as needed)
(8 + 5 )(8 " 5 ) = 64 " 5 = 59
! 34) Multiply (v(5&9) -v(5&3))(v(5&8) + v(5&27)) =
(
!
5
9 "5 3
)(
5
)
8 + 5 27 = 5 72 + 5 243 " 5 24 " 5 81 = 3 + 5 72 " 5 24 " 5 81