- #1
erisedk
- 374
- 7
Homework Statement
Find [(3 - 51/2)/2]1/2
Homework Equations
The Attempt at a Solution
My calculator says (-1 + √5)/2
I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.
blue_leaf77 said:What do you get after multiplying the original expression with ##\frac{\sqrt{2}}{\sqrt{2}}##?
It is √(6-2√5) ÷ 2. Then express the terms under the radical in the form I wrote in post #2, that is, write ##6-2√5 = a^2+b^2-2ab## . FInd the right pair of ##a## and ##b## such that the LHS is equal to RHS.erisedk said:√(6-√5) ÷ 2
An irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers. Examples of irrational numbers include pi (3.14159...) and the square root of 2 (1.41421...).
To simplify a square root of an irrational number, you must find a perfect square factor of the number inside the square root. Then, you can take the square root of that factor and move it outside of the square root symbol.
No, not all square roots of irrational numbers can be simplified. Only those that have perfect square factors can be simplified. For example, the square root of 7 cannot be simplified because 7 does not have any perfect square factors.
The purpose of simplifying a square root of an irrational number is to make it easier to work with and understand. Simplifying allows us to express an irrational number in a more concise and manageable form.
A square root of an irrational number is simplified when there are no perfect square factors left inside the square root symbol. This means that the number cannot be further simplified and is in its simplest form.