how do u do square roots of perfect and imperfect squares?
how do u do the imperfect squares?
To find the square root of a perfect square, you simply need to find the number that, when multiplied by itself, gives you the perfect square. For example, the square root of 16 is 4 because 4 x 4 = 16.
Here's how you can find the square root of an imperfect square:
1. Identify the number as an imperfect square. An imperfect square is a number that does not have a whole number square root.
2. Start by finding the two nearest perfect squares below and above the given number. For example, if you want to find the square root of 12, the nearest perfect squares below and above 12 are 9 (3 x 3) and 16 (4 x 4).
3. Take the square root of the lower perfect square as a starting approximation. In this case, the square root of 9 is 3.
4. Divide the imperfect square by the approximation you just found. For example, divide 12 by 3, which equals 4.
5. Average the result of the division with your approximation. Add the result (4) to your approximation (3) and divide by 2 to get the new approximation. So, (4 + 3) / 2 = 3.5.
6. Repeat steps 4 and 5 with this new approximation until you reach the desired level of accuracy. In this case, dividing 12 by 3.5 will yield a result closer to the actual square root of 12.
You can repeat steps 4 and 5 using a calculator or by hand until you reach the level of accuracy you desire.
How did you know it was a perfect square if you did not know the square root?
If it is not a perfect square, there are lots of different ways to approximate it, including trial and error.
eg
sqrt 5
guess 2.1 --> 4.41
2.2 --> 4.84
2.3 --> 5.29
oh
2.25 --> 5.0625
etc