When you're breaking down the square root in the quadratic formula into several parts- say it was the originally the square root of 80 so you break it down to square root of 4 and square root of 20-would the results be added or multiplyed? Because I know when you further break this down you get 2, the square root of five and the square root of four. Would you add the two 2's, or multiply them? And is there a +/- sign in front of each coefficient or is it just in front of the ACTUAL square root, not the broken down parts of the square root? Thank you so much for clarifying this!
You probably have a something like this
(? ± √80)/??
so when you "break down" the √80 you would look for the largest perfect square which divides into 80. That would be 16
so √80 = √16 x √5
= 4√5 , which means 4 times the square root of 5
when you put that back into the formula expression you would of course keep the ±
get used to checking your work with a calculator.
find √80 and note its decimal answer
now find √5 , then multiply that by 4
You should get the same answer correct to about 8 decimal places, if not, you made a mistake.
When breaking down a square root expression like √80, you can simplify it by breaking it down into smaller factors or perfect squares. In your example, you correctly identified that √80 can be broken down as √(4 * 20).
Now, you can simplify each part separately. The square root of 4 is 2, and the square root of 20 cannot be further simplified unless you break it down into prime factors. √20 can be written as √(2 * 2 * 5), which simplifies to 2√5.
So, √80 can be written as 2√5.
If you have a quadratic equation and you need to use the quadratic formula, it states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this formula, the expression inside the square root, b^2 - 4ac, is what you need to evaluate. If that expression happens to contain a square root like 2√5, then you don't add or multiply the numbers within the square root together. Instead, you leave it as it is, unless further simplification is possible.
Regarding the +/- sign, it applies to the entire expression √(b^2 - 4ac) in the quadratic formula. The sign is placed in front of the square root, not the individual broken-down parts of the square root. The ± sign indicates that you will have two possible solutions, one with a positive value and the other with a negative value.
So, when simplifying the quadratic formula, you evaluate the expression within the square root, keeping any simplified square root expressions intact, and then apply the +/- sign to the final result.
To recap:
- When breaking down a square root expression, simplify each part separately using the properties of square roots.
- In the quadratic formula, evaluate the expression within the square root without adding or multiplying the broken-down parts. Keep any simplified square root expressions intact.
- The +/- sign is placed in front of the square root in the final result, not the individual parts of the square root expression.