2007-01-02 09:58:00 · 14 answers · asked by Sally s 1 in Science & Mathematics ➔ Mathematics
When i'm multiplying brackets out, i use a technique called "boxes". Basically, write out the first bracket along the top of a 2x2 grid, then the second down the left hand side.
Then just multiply the terms when they cross, and add them up at the end.
eg. |______|_____8 _________________+root 3_________|
|____5__| ___5*8 = 40_______|____5*root3 = 5root3____|
|_-root 3_|__8*-root3 = -8root3_|__root3*-root3 = -3_______|
Add the middle bits up: 40 + 5root3 - 8root3 - 3
= 37-3root3
Root 3 is an irrational number, so the answer is irrational i'm afraid.
2007-01-02 10:09:05 · answer #1 · answered by readie252 2 · 0⤊ 0⤋
If you "FOIL" these two factors you get the terms:
8*5 + 5*√3 - 8*√3 - √3√3
40 - 3√3 - 9
31 - 3√3
√3 is irrational, as is the square root of any integer that is not a perfect square (like 4, 9, 16, 25, etc), so the final expression is also irrational.
2007-01-02 10:06:56 · answer #2 · answered by grand_nanny 5 · 0⤊ 0⤋
OK, well if you're wanting to understand math, we'd better brush up on what these symbols really mean. The "square root sign" doesn't always denote square roots. Most people would probably call it a "radical" or "root symbol." The quantity under the radical (in this case, 8) is called the "radicand." It's the quantity whose root we're considering. The smaller number, in this case 3, is called the index. This represents the power of the root that equals the radicand. (For some reason, when we're notating a square root, the 2 is normally omitted.) But when the number is 3, as in this case, it's the cube root we're looking for. In other words, cuberoot(8) = x, such that x³ = 8. In this case, x = 2, because 2³ = 8. So, sqrt(16) + cuberoot(8) = 4 + 3 = 7.
2016-03-29 05:00:45 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Irrational
The answer is 37 minus (3 times the square root of 3)
2007-01-02 10:20:18 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Steps:
( 8 + sqrt 3 ) ( 5 - sqrt 3)
40 + 5 sqrt 3 - 8 sqrt 3 - 3
37 + 5 sqrt 3 - 8 sqrt 3
37 + sqrt 3 (5 - 8)
37 + sqrt 3 ( - 3)
37 - 3 sqrt 3
Answer is irrational...because sqrt 3 is an irrational number. See website under Source(s) below.
2007-01-02 09:59:36 · answer #5 · answered by Piguy 4 · 0⤊ 0⤋
irrational because 3(5 - square root of 3) is irrational. Got what I meant?
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Here is the reason:
(8 + square root of 3) (5 - square root of 3)
= 3(5 - square root of 3) + (5 + square root of 3)(5 - square root of 3)
= 3(5 - square root of 3) + 22
2007-01-02 10:06:14 · answer #6 · answered by sahsjing 7 · 0⤊ 1⤋
Nature Nate is right.
Keep in mind: the square root of any prime number is irrational. A
That product has a sqrt(3) in it and so is irrational.
2007-01-02 10:04:54 · answer #7 · answered by modulo_function 7 · 0⤊ 0⤋
that would be 40 - 3*sqrt(3) - 3
the square root of 3 is irrational, therefore the answer is also irrational
2007-01-02 10:01:08 · answer #8 · answered by Anonymous · 1⤊ 0⤋
Im a math teacher and I dont agree in this but considering I am nice the answer is irrational
2007-01-02 10:12:34 · answer #9 · answered by soccerqt 2 · 0⤊ 0⤋
(8 + sqrt of 3) (5 - sqrt of 3)
= 40 + (8-5)*sqrt of 3 - 3
= 37 - 3*sqrt of 3
it is irrational, because 3*sqrt of 3 is irrational
2007-01-02 10:04:41 · answer #10 · answered by James Chan 4 · 1⤊ 0⤋