Multiplicative inverse help?

Question

Wat is the simplified, exact value of the multiplicatve inverse of 1 minus square root of 2?

Answer 1

Every real number except zero has a unique multiplicative inverse, also known as its reciprocal.

So, you want the reciprocal of 1-sqrt(2), right?

1/(1-sqrt(2)) * (1+sqrt(2))/(1+sqrt(2)) = (1+sqrt(2))/(1-2) =

-1-sqrt(2)

Check

[1-sqrt(2)]*[-1-sqrt(2)] = -1[1-2] = 1 , so it checks

So, the multiplicative inverse of 1-sqrt(2) is -1-sqrt(2)

Answer 2

Assumption: Multiplicative inverse is that number which when multiplied by the number in question yields an answer of one (1)

Assumption: Seeking the multiplicative inverse of (1 - SQR(2))

Answer: 1 / (1 - SQR(2))
Explanation: All you have to do to get the multiplicative inverse in flip your number
Now simplify it: mulitply the top and bottom by (1 + SQR (2) ) which leaves numerator of ( 1 + SQR (2) ) and denominator of negative one (-1) after the multiplying and cancelling in the denominator. So the final answer is ( -1 - SQR(2) ).
Disclaimer: It's been twenty years since I took algebra. Hope that was right. Sorry if it's not

Answer 3

The given number is (1-sqrt(2))
The inverse needed is 1/(1-sqrt(2))
Multiply by the conjugte (1+sqrt(2)) both numerator and denominator to get:
(1+sqrt(2))/[(1+sqrt(2))*(1-sqrt(2))] and notice that

[(1-sqrt(2))(1+sqrt(2))] = 1^2 - [sqrt(2)]^2 = 1 - 2 = -1
since this is a square difference a^-b^2= (a-b)(a+b)

So the inverse is [(1+sqrt(2))]/-1 = -1-sqrt(2)

Answer 4

basically we have to find 1/(1-(2)^0.5))
multiply both numerator and denominator by 1+(2)^0.5
the denominator will simplify to -1 as (a+b)(a-b)=a2-b2
therefore 1^2-2=-1.
therefore the answer will be -(1+(2)^0.5)
-2.414( taking square root of 2 as 1.414

Answer 5

1 / (1 - sqrt2)
multiply top and bottom by 1 + sqrt2 to get the sqrt out of the denominator
(1 + sqrt2) / (1 - sqrt2)(1 + sqrt2)
= (1 + sqrt2) / (1 + sqrt2 - sqrt2 - 2)
= (1 + sqrt2) / -1
= -1 - sqrt2

funny how that works

Answer 6

-1 - sqrt(2)

Answer 7

1/(1-sqrt(2)) = -1-sqrt(2)