√√2-1/√2+1
√2-1
I will assume you meant:
√(√2 - 1) )/(√2 + 1) , which when evaluated by calculator = appr. .26658..
let x = √(√2 - 1) )/(√2 + 1)
square both sides,
x^2 = (√2 - 1)/(2 + 2√2 + 1)
= (√2 - 1)/(3 + 2√2)
= (√2 - 1)/(3 + 2√2) * (3 - 2√2)/(3 - 2√2)
= (3√2 - 4 - 3 + 2√2)/(9 - 8)
= 5√2 - 7)
√(√2 - 1) )/(√2 + 1) = √( 5√2 - 7) which is appr .26658... as expected
The answer given by anonymous is incorrect
To simplify the expression √√2 - 1/√2 + 1, we can follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Starting with the expression:
√√2 - 1/√2 + 1
1. Simplify the first part √√2.
√√2 = (√2)^(1/2) = 2^(1/4)
2. Simplify the denominator 1/√2.
1/√2 = √2/2
Now, re-write the expression:
2^(1/4) - √2/2 + 1
Since there is no further simplification to be made, we can now find the common denominator to add the fractions.
3. Obtain the common denominator for the fractions.
The common denominator for 2 and 1 in the denominators is 4.
Rewrite the expression with a common denominator:
2^(1/4) - (√2/2)(2/2) + (1/1)(4/4)
Now simplify:
2^(1/4) - 2√2/4 + 4/4
4. Simplify each term in the expression.
2^(1/4) can be written as the fourth root of 2. So,
2^(1/4) = ∛∛∛2
Final expression:
∛∛∛2 - (2√2)/4 + 4/4
Simplifying further is difficult since the terms involve the fourth root and square root of 2. Hence, this is the simplest form of the expression:
∛∛∛2 - (2√2)/4 + 1