To be able to add and subtract numbers with square roots, the square roots of the numbers must be the same. If you have different square roots, you must convert them to the same square root if you can, and if you can’t, remember that you cannot add and subtract. For example, the numbers 3√3 and 5√3 can be both added and subtracted, but the numbers 3√3 and 3√5 cannot be added together. Just keep on reading to learn in detail how to add and subtract numbers with equal square roots or numbers that can be equalized.
Basic Operations
- Simplify the inside of square roots as much as possible. Find the squared numbers to take out the numbers inside the square roots and make the square roots easier. For example, try to find numbers like 16 (4 x 4), 9 (3 x 3). When you find numbers in this way, you can take them out of the square root and simplify the square root. If we examine in more detail through an example: If we look at how to simplify the square root expressions for the sum of 7√50 – 3√8 + 6√12,
- 7√50 = 7√ (25 x 2) = 7√ (5² x 2) = (7 x 5) √2 = 35√2. Here, if we factor the number 50 into 25 x 2, you will see that 25 is the square of 5. The number 25 goes out of the square root as 5. The thing to do now is to put the number 5 next to the number 7 and do this multiplication: 7 x 5 = 35.The number outside the square root (the square root coefficient) is now 35, and the number 2 is left in the square root: “2”
- 3√8 = 3√ (4 x 2) = 3√ (2² x 2) = (3 x 2) √2 = 6√2. In this process, if we express the number 8 as 4 x 2 in the square root, it will be seen that the number 4 is the square of 2 (4 = 2 x 2). From here the square root number 4 comes out as 2 outside the square root. Now the number 2 is multiplied by the number 3 except the square root: 2 x 3 = 6. We found the square root coefficient to be 6 and the number in the square root to be 2 (2).
- 6√12 = 6√ (4 x 3) = 6√ (2² x 3) = (6 x 2) √3 = 12√3. In this process, the number 12 in the square root can be factored into 4 x 3. Since 4 is the product of 2 by 2, it leaves the square root as 2. It is then multiplied by the coefficient of the original square root (2 x 6) = 12 new square root coefficients are found. Since the number 3 remains in the square root, the new square root value becomes 3 (3).
- Circle the summable square root expressions. Show the summability of your simplified square root expressions by circling the numbers in the square root: 35√2 – 6√2 + 12√3. In the example we have given, since the numbers 35√2 and 6√2 have the same square root values, the square root coefficients can be derived normally. You can add both numbers in the same way. The only thing to know is that if the square-rooted numbers are the same, those two numbers can be added and subtracted. It’s like direct addition of fractions with the same denominator.
- If you are adding or subtracting more square root numbers, and there are several numbers in which the numbers in the square root are the same, then show each additive number with a different symbol. For example: Mark numbers with √3 with the symbol “*”. Underline the numbers with 5 and circle the numbers with √2. In this way, you will be able to detect which numbers can be added much more easily.
- Add or subtract the square root numbers where the numbers in the square root are equal. Now all you have to do is add / subtract the additive / subtractable square-root numbers, then leave the non-additive square-root numbers as they are. If operations are done on the example we gave in steps 1 and 2:
- 35√2 – 6√2 + 12√3 =
- (35 – 6)√2 + 12√3 =
- The result of the process is found as 29√2 + 12√3.
Video:
Tips:
- You should get into the habit of simplifying before adding or subtracting square root numbers. In this way, you will have done the transactions much faster.
Warnings:
- Never try to add square root numbers where the numbers in the square root are not the same.
- 4 + (3x)1/2 cannot be a simplified form of any square root number.
Farklı Diller
Hazırlayan: A. Kadir
Kaynak: 1 (Erişim: January 18, 2020) 2 (Erişim: January 18, 2020)