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**Question:**Need help with algebra, roots of real numbers and radical expressions? the negative square root of 89 the negative square root of 324 Simplify the square root of 16m squared over 25 the third root of 216p^3q^9 the fifth root of -32x^5y^10 the fourth root of (x-5)^8 the third root of -432 the third root of -5000 the fourth root of 48v^8z^13 the square root of 11/9 the square root of 9a^5/64b^4 (2 times sqrt of 24(7 time sqrt of 18) 8 sqrt of 48 - 6 sqrt of 75 + 7 sqrt of 80 (sqrt of 5 - sqrt of 6)(sqrt of 5 + sqrt of 2) (sqrt of 3 + 4 sqrt of 7)^2 6/ sqrt of 2 - 1 3 + sqrt of 6/5 - sqrt of 24

**Answers:**Hi, the negative square root of 89 - 89 does not factor or simplify the negative square root of 324 - 324 = -18 the square root of 16m squared over 25 (16m /25) = 4m/5 the third root of 216p^3q^9 (216p^3q^9) = 6pq (6pq^3) the fifth root of -32x^5y^10 -2xy the fourth root of (x-5)^8 (x - 5) the third root of -432 -6 (2) the third root of -5000 -10 (5) the fourth root of 48v^8z^13 . . . . . ___ . . . .4/ 2v z \/ 3z the square root of 11/9 (11)/3 the square root of 9a^5/64b^4 . . . _ 3a a --------- 8b (2 times sqrt of 24(7 time sqrt of 18) 2 24(7 18) = 4 6(21 2) = 84 12 = 168 3 8 sqrt of 48 - 6 sqrt of 75 + 7 sqrt of 80 8 48 - 6 75 + 7 80 = 32 3 - 30 3 + 28 5 = 2 3 + 28 5 (sqrt of 5 - sqrt of 6)(sqrt of 5 + sqrt of 2) ( 5 - 6)( 5 + 2) = 5 + 10 - 30 - 12 = 5 + 10 - 30 - 2 3 (sqrt of 3 + 4 sqrt of 7)^2 (3 + 4 7) = (3 + 4 7)(3 + 4 7) = 9 + 24 7 + 16 49 = 9 + 24 7 + 16(7) = 9 + 24 7 + 112 = 121 + 24 7 6/ sqrt of 2 - 1 . .6 --------- = 2 - 1 6( 2 + 1) ---------------------- = ( 2 - 1)( 2 + 1) 6( 2 + 1) -------------- = 6( 2 + 1) 2 - 1 3 + sqrt of 6/5 - sqrt of 24 3 + (6/5) - 24 = 3 + (30)/5 - 2 6 I hope that helps!! :-)

**Question:**Square root of 144x^3y^4z^5

**Answers:**"Absolute value symbols"? How do they come into it ? (144 x^3 y^4 z^5) = (144 x^3 y^4 z^5)^ = 12 x^(3/2) y z^(5/2)

**Question:**I've been working on these problems for a little over an hour and i can't for the life of me figure out how to do them. Can someone walk me through these? Hopefully i'll start to get the hang of it. (-2 15)(4 21) 3 ^3 128 + 5 ^3 16 --- ^ indicates an index (50x^4 ) ---- ^ indicates an exponent Thanks!

**Answers:**These depend on the directions instructing to keep in simplest radical form or take to a decimal. These will be in simplest radical form. 1.) (-2 15)(4 21) = -8 315 {multiply} = -8 9 35 {depending on the directions whether to take to a decimal or not} = -8(3) 35 {square root of 9 is 3} = -24 35 {multiply} 2.) 3 128+5 16 ==3 64 2) + 5 8 2 {break down the cube roots again directions dependent} = 3(4) 2 {cube root of 64 is 4} = 12 2 {multiply 3 by 4} 3.) 50x^4 = 25x^4 2 {group the perfect squares together under one square root sign} = 5x^2 2 {take the square root of 25x^4} More like this can be found here under "Other Radicals" at: http://algebra2notes.weebly.com/ch--6-radicals-and-rational-number-exponents.html

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