How do you get the square root of 196?

Answer 1

To find a square root mathematically or manually, you must use a special adaptation of long division. The link suggested below looks complicated but is actually very easy to follow. Try the long division method to find the square root of 196, which is 14, of course. You also could have easily guessed the answer, if you remember that "15 x 15 is 225" ( too big a number ). So drop down to the next lower number and multiply it by itself, to see if you get closer to the target square of 196. BINGO !!! It's very tiresome / difficult to type out the long explanation, but very easy for you to follow the simple directions. You'll be glad you did. Step 1: Click on your Start Menu button

Step 2: Find the 'Calculator' application under 'Accessories' and click on it.

(Or find the equivalent application if you're using a Mac/Linux)

Step 3: Type in the numbers '1, 9, 6' (in that order).

Step 4: Push the 'sqrt' button.

Step 5: Read the number that appears in the little box.

Step 6: Give yourself a gold star for the good work!

Note : if the calculator does not have a 'sqrt' button but does have an x^y button, just remember that square roots are 1/2 powers-- x ^(.5) is the square root of x.

Alternate: There is a longhand method available for those times when your battery is dead or your computer has died. See Link. Slide rules and log tables will work as well.

There is an algorithm based on the binomial series for 1/2 powers. It look somewhat like long division but is hard to do on keyboard

First you break the number into groups of two starting at decimal point. ---------

1 96 find the approximate square root of the first group, 1 in this case so 1 is the first digit of the answer. Double this first value, to get 2 and add 0 to it ,mentally. Divide 20 into 96 and get 4 -- but here where this process differs from long division :: add the 4 to the 20 to get 24 and multiply 4 time 24 , not 4 time 20, as you would in long division, subtract from the 96. Since 4 * 24 = 96, you are done. 14 is the exact answer. If 4* 24 would have been larger than 96, you would try 3.

If the number is not a perfect square, you can carry out the process to as many decimals are you wish,by adding zeroes in blocks of 2 . Another example. Find the square root of 2100 to two decimal places

Think of the number as 2100. 00 00 and block it off into groups of 2: 21 00 . 00 21 00 . 00 16 5 00

The approx. square root of 21 is 4, so 4 is the first digit of the answer. Compute

4 squared and subtract from the 21 to get 5 .

Double the 4 to get 8, drop down the two 0's and find a trial divisor -- what is 80 into 500 ?

About 6? but 6 is too big, since you have to add the 6 to the 80 -- 86 * 6 = 516 - too big, so 5 is what you want-- the next digit in the answer is 5. 85 * 5 = 425 and subtracting form 500, get 500-425 = 75. The answer is 45 and a fraction. To the first decimal , double the 45 to get 90 , drop down two zeroes and ask what is 90 into 7500 ? 8 works 908 * 8 = 7264. So, the answer is 4 To get the next decimal place, subtract : 7500 -7264 = 236

double 458 to get 916 and divide 9160 into 236 00 . 2 works since 9162 * 2 = 18 324, so the final answer is 45.82 truncated to two decimal places.

Answer 2

1.4 x 1.4 = 1.96