course Math 158
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3. T or F 5 the square root sign (with this 5 in the check mark part of the square root sign) then a -32 inside the square root = -2
This is false because the 5 would have to be a multiple of 4 to make the answer come out correctly.
Simplify expression - Assume that all variables are positive when they appear.
6. 4 is in the check part of the square root sign and 16 is inside the square root. The answer is 2
9. square root of 8 = inside the square root sign is 4 times 2 = 2 outside of thesquare root sign and 2 inside the sign
12. 4 is in the check mark part of the square root sign and 48x^5 is inside the square root = 4 is still in the check mark part of the square root with 16 times 3x^5 inside of the square root sign = 2 and then the 4 still in the checkmark part of the square root sign with 3x^5 inside the square root =
2x then the 4 in the checkmark part of the square root sign and 3x inside of the square root
15. A big square root sign with 4 in the check mark part and inside the square root sign x^9y^7 4 inside of the check mark and x8y^4 inside the square root sign = 4 inside the checkmark and x8 inside of the square root sign times 4 in the checkmark and y4 inside the square root sign
= x^2y^1
_________ =
xy^3
18. The square root of 9x^5 = 3 and then the square root sign with x^5 inside = 3x^2 outside the square root sign and x inside = The square root of 9 = 3
20. The square root of 5x and the square root of 20X^3 = The square root of 100X4 = (10x^2)
23. (3 outside the square root sign and 6 inside it) (2 outside and 2 inside) = 12 on the outside and 3 inside
26. 6 outside the check mark and 5 inside the square root sign - 4 outside and 5 inside = 2 on the outside and 5 on the inside
29. (the square root of 3 + 3) (the square root of 3 - 1) = 2 outside the check mark and 3 inside the square root sign
32. ??
37. The square root sign with 8x^3 - 3 outside the check mark and 50x inside , x > or equal to 0
Inside the square root is 4 times 2x^2 times x - 3 on the outside of the check mark and 25.2x on the inside = 2x on the outside and 2x on the inside - 15 on the outside and 2x on the inside =
2x on the inside (2x - 15)
39. ??
42. 2/square root of 3 times square root of 3/square root of 3 = 2outside the check mark and 3 inside the square root sign/square root of 9 =
2 outside the checkmark and 3 inside the square root sign/3
46. square root of 2/ square root of 7 + 2 = square root of 2/square root of 9 = square root of 2/3^2
49. 5/3 above the check mark and 2 inside the square root sign = 5 next to the checkmark with 3 above it and 4 inside the square root sign/2
52. ??
Simplify.
55. (-27)^1/3 = -3
58. 25 ^2/3 = (25)^3/2 = 5^2
61. (9/8)^3/2 = (9)^3/2 = (3^2)^3/2 = 3^6/2
________ __________ ________
(8)^3/2 (2^3)^3/2 2^9/2
64. (8/27) ^-2/3 = (8)^-2/3 = (2^3)-2/3
___________ _____________
(27)^-2/3 (3^3)^-2/3
Simplify - Express answers so that only positive exponents occur.
67. (x^3)y6)^1/3 = (x^3)^1/3(y^6)^1/3 = xy^2
70. (xy)^1/4 (x^2y^2)^1/2 = (x^2)^1/2(y^2)1/2(xy)^1/4 = (xy^2)
72. ??
Write each expression as a single quotient in which only positive exponents and/or radicals appear.
76. ??
79. the square root of 1+x - 1/2 outside the checkmark and 1 + x inside the square root / 1 + x , x > -1
2(1+x)-x/2(1+x)^1/2 times 1/1+x = 2+x / 2(1+x)^3/2
82. ??
85. ??
90. ??
Factor each expression.
93. 4(3x+5)^1/3(2x+3)^3/2+3(3x+5)^4/3(2x+3)^1/2 , x> or equal to -#/2 =
(3x+5)^1/3 (2x+3)^1/2 [4(2x+3) = 3(3x + 5)] = (3x + 5)^1/3 (2x+3)^1/2 (8x+12+9x+15) =
(3x+5)^1/3 (cx+3)^1/2 (17x+27)
96. 8x^1/3 - 4x^-2/3, x does not equal to 0 = 4x^1/3
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You also seem to know what you are doing here, but you are not using the correct 'typewriter' notation and I cannot read through your work quickly enough to see the details.