How can I get a square root from a number (manually)? I knew the system but I just forgot it.?

Answer 1

http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Answer 2

I learned it once too, and have forgotten it. Of course, they don't teach it anymore. Fortunately, I have an old college algebra book. Here's what it says ...

To find the square root of a number, written in decimal notation:

1. Separate the number into groups (or periods) of two figures each, both ways from the decimal point. Hereafter, count groups from left to right.

2. Below the first group, write the largest perfect square less than that group. Above the group, write the square root of this perfect square.

3. Subtract the perfect square from the first group; bring down the next group, thus forming the first remainder.

4. Form the trial divisor by doubling the part of the root now found, and annexing zero. Divide the first remainder by this trial divisor, taking as the quotient only the whole number obtained. (Possibly reduce the number by 1.)

5. Form the complete divisor by adding to the trial divisor the new figure of the square root found in Step 4.

6. Multiply the complete divisor by the new figure of the square root. Write the product under the remainder. Subtract.

7. Continue in this way, following Steps 4 to 6, until the remainder is zero, or until you have as many places in the square root as are requested.

[Whew! After that, I know why it's not taught anymore!]


Example 1. Find the square root of 7569.

Step 1. Arrange it in groups 75 69. Write the largest perfect square, 64, below the 75, and write the square root, 8, above the 75. Subtract 64 from 75 to get 11, and bring down the next group to get 1169

Step 2. Form the trial divisor, 160, by doubling the 8 and appending a 0.

Step 3. Divide the 160 into the 1169 (equals 7+) to form the complete divisor, 167. Write the 7 above the second group (the 69).

Step 4. Multiply 7 x 167 = 1169. Subtract 1169 from 1169. Since that's zero, the square root of 7569 is 87.


Example 2. (Both of these examples are taken from the book.) Find the square root of 645.16.

Step 1. Break it into groups: 6 45. 16. Write the largest square, 4, below the 6, and write the square root, 2, above the 6. Subtract 4 from 6 to get 2, and bring down the next group (45) to form 245.

Step 2. Double the root 2, and append a 0, to form the trial divisor 40. 40 goes into 245 6 times, but 46 x 6 > 245, so we must reduce the quotient by 1 to a 5. Write the 5 above the second group (45) and form the new divisor, 45. Multiply 45x5 = 225, and subtract the 225 from 245 to get 20. Bring down the next group (16) to form 2016.

Step 3. Double the root 25, and append a 0, to form the trial divisor 500. 500 goes into 2016 4 times, and 4 x 504 = 2016. Write the 4 above the third group (16), and subtract the 2016 from 2016 to get 0.

The square root of 645.16 is 25.4

Answer 3

Do a tree. Say the number is 300, you'd say that is 150 and 2 then you break down 150 which would be 75 and 2 then break down 75 and thats 25 and 3 then break down 25 and thats 5 and 5. So you'll have two 2's and since its square root they cancel out, then you'll have two 5's and they "cancel out". That leaves you with a 3. That goes on the outside. Then you take the 2 times the 5 and that equals 10. soo it'd be 3 on the outside and 10 on the inside. I know it's confusing, but do it on paper, you might get it!

Answer 4

In mathematics, a square root of a number x is a number whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted \sqrt x. For example, the principal square root of 9 is 3 (denoted \sqrt 9 = 3) because 3^2 = 3\times3 = 9. The other square root of 9 (not the principal square root) is −3.

Answer 5

Okay say the number is N.
estimate the square root, call it a.
Find N/a. Take the average of a and N/a.
That is your new estimate. Repeat.
Keep repeating. The estimates will get closer and closer.

Answer 6

Try finding its factors, and then take the common factors and multiply eg. 1225=5x5x7x7=5x7=35 now 35x35=1225

Answer 7

http://www.math.com/school/subject1/lessons/S1U1L9DP.html