111. Extracting the square root

The lesson, step by step

1. Warm-up

   Square 42 by the tens-and-units pattern: 1600 + 160 + 4 = 1764.

2. The second explanation

   Read:

   We learned in Art. 371 that the square of a number composed of tens and units is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.

   So for √1764: the tens are 4 (1600). The 164 left over is (80 + units) × units. Try 2: 82 × 2 = 164. The root is 42.

3. The rule

   Read the first steps:

   Point off the number into periods of two figures each, commencing with units.

   Find the greatest square in the first period on the left; place its root on the right, like a quotient in division.

   Double the root already found, as if it were units, and write it on the left for a trial divisor.

   Work √11881 together, following the rule step by step.

4. Notes

   Read:

   If any product be found too large, the last figure of the root is too large.

   The number of decimal places in the power must be even.

   SayFor decimals, pair off from the decimal point both ways, adding a zero if needed.

5. Practice

   Your student works several of the examples, such as √1444, √3444736 and √57600, then √3 to seven decimal places.

6. Products and fractions

   Read:

   The square root of a common fraction is equal to the square root of the numerator, divided by the square root of the denominator.

   It is advantageous to multiply both terms by what will render the denominator a square.

   Try one fraction example from the book.

7. Check and wrap-up

   Check the printed answers by squaring each root. Ask: How do you know √3 can never come out exactly?