To simplify this expression, we can use the difference of squares formula which states that (a + b)(a - b) = a^2 - b^2. In this case, a is sqrt(2) and b is 1. Therefore, we can rewrite the expression as (sqrt(2) + 1)(sqrt(2) - 1). Using the formula, we get (2 - 1) which simplifies to 1. This leaves us with the simplified expression of 2 + sqrt(2).
The difference of squares formula is used to simplify expressions involving square roots. It allows us to eliminate the radical sign and simplify the expression to a more manageable form. In this case, it helps us to convert the division of two square roots into a sum of two square roots, making it easier to evaluate the expression.
No, we cannot simplify this expression to a whole number. The simplified form of 2 + sqrt(2) is an irrational number, which means it cannot be expressed as a fraction or a whole number. This is because the original expression contains an irrational number (sqrt(2)) and dividing it by another irrational number (sqrt(2) - 1) will result in an irrational number.
Yes, we can use a calculator to verify the simplification of this expression. However, it is important to note that calculators may not always give the exact simplified form because they use approximations. It is always best to understand the mathematical concepts behind the simplification process.
Yes, there are other methods to simplify this expression. One method is to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which in this case is sqrt(2) + 1. This will eliminate the square root in the denominator, and we will be left with 2 + sqrt(2). However, the difference of squares formula is the most efficient method to simplify this particular expression.