I get confused when solving for some of the fractions in my problem. how would you solve for 1+(-2/(sqroot 5))? I just need a refresher on the order of operations for it. Thanks!
when you have a term squareroot (for example sqrt(x))in the denominator, multiply it with itself such that the multiplier is equal to one ( sqrt(x)/sqrt(x) ) to remove the squareroot,, in this problem:
1+(-2/(sqroot 5))
1+(-2/(sqroot 5))*(sqrt(5)/sqrt(5))
1+{[-2*sqrt(5)]/5}
therefore:
{[5-2*sqrt(5)]/5}
so there,, :)
To solve the expression 1 + (-2 / √5), you can follow the order of operations, which is commonly remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
1. Simplify any expressions inside parentheses. In this case, there are no parentheses.
2. Next, evaluate any exponents. There are no exponents in this expression.
3. Proceed with multiplication and division from left to right. In this expression, you have a division operation: -2 / √5.
To simplify this division, you need to rationalize the denominator. Rationalizing the denominator means removing any square roots or radicals from the denominator.
In this case, the denominator is √5. To rationalize the denominator, you need to multiply the numerator and denominator by the conjugate of the denominator - in this case, √5 itself. By multiplying the numerator and denominator by √5, the denominator will become a rational number (without any square roots).
So, (-2 / √5) can be simplified as follows:
(-2 / √5) * (√5 / √5) = -2√5 / (√5 * √5) = -2√5 / 5
4. Now that the division has been simplified, you can proceed with addition and subtraction from left to right. In the expression, you have 1 + (-2√5 / 5).
To add 1 and -2√5 / 5, you need to find a common denominator. In this case, the common denominator is 5. So the expression becomes:
(5 * 1 + (-2√5)) / 5 = (5 - 2√5) / 5
Thus, 1 + (-2 / √5) simplifies to (5 - 2√5) / 5 after following the order of operations and rationalizing the denominator.