Solve Math Problem II: 3 - (Square Root of 2)

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In summary, the conversation is about finding the square root of 11 - 6*(square root of 2) and writing the solution in surd notation. The answer provided by the book is 3 - (square root of 2) and the suggestion is to use binomial expansion to solve the problem. The conversation also discusses finding a perfect square of some binomial and solving for its components. The final solution is found using ( [squ] x - [squ] y ) to the power of two.
  • #1
denian
641
0
i tried this. but fail to get the answer


find the square root of 11 - 6*(square root of 2) and write the solution in surd notation.


answer provided by the book :
3 - (square root of 2)
 
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  • #2
My calculator gives the answer to be 3-sqrt(2).

Why don't you try using binomial expansion to solve the problem.

sqrt(11-6*sqrt(2)) = sqrt(11)*(1+((-6/11)*sqrt(2))^(1/2)

x = (-6/11)*sqrt(2)
n = 1/2

1 + n*x + (n*(n-1)*x^2)/2! + (n*(n-1)*(n-2)*x^3)/3! + ...
 
  • #3
You want 11 - 6√2 to be a perfect square of some binomial. Since you have that -6√2 term, look for a binomial such that
(a - b√2)2 = 11 - 6√2

What happens when you multiply out
(a - b√2)2 ?

Can you solve for a and b?

Does that help?
 
  • #4
yup.
thanks.
 
  • #5
but i use ( [squ] x - [squ] y ) to the power of two instead.
 

1. What does "3 - (Square Root of 2)" mean?

The expression "3 - (Square Root of 2)" means to subtract the square root of 2 from the number 3. This can also be written as 3 - √2.

2. How do I solve "3 - (Square Root of 2)"?

To solve this expression, you can use a calculator or manually calculate the square root of 2, which is approximately 1.414. Then, subtract 1.414 from 3 to get the final answer of 1.586.

3. Can the answer to "3 - (Square Root of 2)" be simplified?

Yes, the answer can be simplified to 1 + √2 or 1.414 + 1. This is because both 3 and the square root of 2 are irrational numbers and cannot be simplified further.

4. What is the difference between "3 - (Square Root of 2)" and "3 - Square Root of 2"?

The parentheses in the first expression indicate that the square root of 2 should be subtracted from 3 as a whole, while in the second expression, only the number 2 is being square rooted and then subtracted from 3.

5. Can "3 - (Square Root of 2)" be written as a decimal?

Yes, the answer to this expression, 1.586, can also be expressed as a decimal. However, it is important to note that the square root of 2 is an irrational number and its decimal representation is infinite.

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