From Omilili

### Simplifying a **radical** expression with all variables

Expression simplifies as . However, since the square is never negative, the **absolute**-

**value**bars aren't needed, and you end up with your final result. I make the big deal about the

**absolute**-

**value**bars of the two

**radicals**into one (since they have the same index). Thank you! Ok, holidays are over, back

From Yahoo Answers

**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:**Simplify. Sqr= square root (-3sqr24)(5sqr20) A. 15sqr480 B. -60sqr30 C. -240sqr30 D. -15sqr480 I think its D, but I dont know for sure!

**Answers:**First, isolate the rationals and radicals. You can do this because of the associative property. (-3 * 5) * (sqrt(24) * sqrt(20)) You can multiply two radicals together -15 * sqrt(24 * 20) You may be able to reduce it. -15 * sqrt(480) -15 * sqrt(16 * 30) -15 * 4sqrt(30) -60sqrt(30) You could have started by simplifying both radicatls -3sqrt(24) * 5sqrt(20) = -6sqrt(6) * 10sqrt(5) Sometimes, though, even when you do that, you still have to simplify the result. Suppose you have sqrt(15) * sqrt(18) Neither one can be simplified alone, but since both radicals contain sqrt(3), when multiplied together you can factor out 3.

**Question:**Okay so the problem is 4(radical sign)10x3(radical sign)6 I'm so lost

**Answers:**What's a radical sign? I forgot already.... :P Ooh. Square root. Imma try this. 4 10 x 3 6 -Is this the problem? Like 4 10 then multiply to that 3 6? 4x3 10x6 -Product Property of square roots, and multiplication property or whatever. You can multiply the ones outside the radical sign together, and the ones inside together. 12 10x6 - Multiply the ones outside together, you can multiply the ones inside, but you will just be taking it apart anyway. 12 2x5x2x3 - Factor out the numbers inside. You can put them in order, 2x2x3x5. 12x2 5x3 - Move the two to the outside. 2x2=4, and the perfect square root of 4 is 2. You move the perfect square root of four outside because it no longer belongs inside. 24 15 - Simplify. Multiply the 12x2, then the 5x3. There are no doubles under the radical sign, so no more moving is needed.

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