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14 Sep 15 10:36
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Date Joined: 19 Feb 03
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(9 / ?)Square root 3 = -27

What is the correct method to work it out please?
Pause Switch to Standard View Maths question Report September 14, 2015 10:44 AM BST
(9/x)root3 = -27  is that the equation.

REckon x = root3 over three then.

9root3 = -27x  (multiply both sides by x)

-(9root3 over 27) = x   (divide both sides by -27)

-root3/3  = x  (divide top and bottom of left side by 9)
Report September 14, 2015 10:47 AM BST Report September 14, 2015 1:15 PM BST
Is it 27?

If the first bracket was 3 youd get 27 so does that mean getting -3 in the first bracket (9/27) gets minus 27?
Report September 14, 2015 2:01 PM BST
doesnt minus 27 fook things up with imaginary numbers Report September 14, 2015 2:22 PM BST
? = -0.577350269189626
Report September 14, 2015 2:28 PM BST
What does square root3 mean? 3 times the square root of the number in the bracket? The cube root of the number in the bracket?
Report September 14, 2015 3:41 PM BST
Brendan is right, the square root of a negative number has an i component.
The square root of a positive number has two solutions, one positive, the other negative.
Report September 14, 2015 3:47 PM BST
I am rusty but perhaps cross multiplying to get

(9sqrt3)/(-27)=x=-sqrt3^-1
Report September 14, 2015 3:49 PM BST
-3  ?
Report September 14, 2015 4:01 PM BST
(9sqrt3)/(-27)=x simplifies to -sqrt3/3 = x (Rob Dylan's solution)

This is - sqrt(+3)/3 =x so is not imaginary and has two solutions positive and negative rendering the inital negative superfluous.
Report September 14, 2015 4:10 PM BST
I read it as cube root, not 'multiply by sqrt of 3'
Report September 14, 2015 4:12 PM BST
- sqrt3^-1
Report September 14, 2015 4:34 PM BST
Sorry, don't know where you get that from dunlaying.
Report September 14, 2015 4:40 PM BST
I have probably been clumsy as Rob Dylan has written it -sgrt3/(3).
If you cross multiply and cancel you will see that the answer is negative, I hope.
Report September 14, 2015 4:47 PM BST
Yes, -sqrt3 =3x
sqrt3 = 1.732 and -1.732
as does -sqrt3

(hope that's right)
Report September 14, 2015 4:58 PM BST
(9/x) multiplied by sq rt 3 = -27
(9/x) multi by 1.73 = -27
divide both sides by 1.73
9/x = -27/1.73
9/x = -15.61
multi both sides by x
9 = -15.61x
9/-15.61 = x
-0.58 = x (I think)
Report September 14, 2015 6:14 PM BST
x = -0.58 and +0.58 (see my previous post)
Report September 14, 2015 7:05 PM BST
9/x × √3 = -27
9√3 = -27x
(9√3)/(-27) = x
X =-0.577 or 0.577

As Foinavon points out, the square root of 3 has two values, 1.732 and - 1.732
Report September 14, 2015 7:31 PM BST
Of course a square root can be positive or negative but in this case the answer is negative.
Take the original equation and you have a positive multiplied by an unknown equal to a negative. Since a positive multiplied by a positive is positive it follows that the unknown be negative.
Report September 14, 2015 7:46 PM BST
Dunlaying you are correct. To get the negative answer the unknown must be negative (-0.577)
Report September 14, 2015 8:03 PM BST
Which part of the LHS is positive? Both 9/x and sqrt3 can be either. If one is +ve the other is -ve.
Report September 14, 2015 8:15 PM BST
To clarify
if 9/x is positive, sqrt 3 is negative.
if 9/x is negative, sqrt 3 is positive.

x is both + 0.577 and -0.577
Report September 14, 2015 9:12 PM BST
Answer is -[3 / (sqrt 3)]
Report September 14, 2015 9:27 PM BST
x = the square root of 3, divided by minus 3

If the square root is taken to be the positive one, then x is a positive divided by a negative, which is a negative number.

If the square root is taken to be the negative one, then s is a negative divided by a negative, which is a positive number.

So x has two values, a positive one and a negative one.

I agree with Foinavon imo.
Report September 14, 2015 9:31 PM BST
What is the square root of 69...............it's ate something...........hold on it's ate.30662386291

I'll get me coat
Report September 14, 2015 10:33 PM BST
Here's how I would do it...might be a bit more long winded but its how I was taught

(9 / ?)Square root 3 = -27 ....the problem

(9/x)(√3) = -27 ...............next move substitute √3 (which is 1.73)
(9/x)(1.73) = -27...............next move is to get the x fraction isolated on one side of the equal sign

9/x = -27/1.73..............next step cross multiply to get rid of fractions (multiply -27 by x and multiply 9 by 1.73)

-27x = 15.57...............next divide both sides by -27 to find x

x = 15.57/-27................calculator time

x = -0.57................answer (plus the Foinavon thisg above...can also be a positive value 0.57)
Report September 15, 2015 7:51 PM BST
Go back to basics and you will find that a number divided by a fraction is the same as that number multiplied by the reciprocal of the fraction eg (2x3) divided by (1/2) =6x(2/1) =12 , x being the multiplication sign.
If you substitute the two answers in our original question you find that -(sqrt3)^-1 gives -27 on the left hand side and -27 on the right hand side which is an equation.
If, however, we substitute +(sqrt3)^-1 in our original question we find that the LHS reads as +27 and the RHS as -27 which is not an equation.

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