How do you simplify square roots? Like how can you get sqrt28 to be 2sqrt7?
a number like √28 can be changed to a mixed radical by looking for factors of 28 which are perfect squares
perfect squares are 4,9,16,25,36,49,64,...
since 28 = 4x7
√28 = √4 x √7
= 2√7
splitting 28 up into factors that do not contain a perfect square, does us no good.
e.g.
√28 = √2 x √14 , nothing gained here.
If a number does not contain a perfect square number it cannot be changed into a mixed radical
Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the first equation should be? What about the second equation? How are these examples similar? How are they different? Find a problem in the text that is similar to examples 2, 3, and 4. Post the problem for your classmates to solve.
To simplify square roots, you need to look for perfect square factors within the number under the radical sign. Here's how you can simplify √28 to 2√7:
1. First, identify any perfect square factors of 28. The perfect squares up to 28 are 1, 4, 9, 16, and 25.
2. Among these, the largest perfect square that divides into 28 is 4 (since 4 is a factor of 28). So, we can write 28 as 4 × 7.
3. Now, rewrite the square root of 28 as the square root of 4 × 7: √(4 × 7).
4. According to the properties of square roots, we can break down the square root of the product by separating them: √4 × √7.
5. The square root of 4 is 2, so we have 2√7.
6. Therefore, the simplified form of √28 is equal to 2√7.
By finding the largest perfect square factor (in this case, 4) that divides into the given number (28), we can express the square root in a simplified form by moving the perfect square factor outside the radical sign.