(a) Finding the square root of 65536, a perfect square:
Take a pencil and paper and follow the steps provided.
- Write the number as if it were the dividend of a dividing question, but place a square root sign to the left.
- Separate the digits of the number 65536 in pairs by commas, counting from the right. The result will be 6,55,36. Note that there is one incomplete pair.
- What number multiplied by itself is equal to 6 or a number just below 6? It will be 2, as 2×2=4.
- Place 2 above the 6 AND in the normal place of a divisor. Multiply 2×2 and place 4 beneath the 6. Draw a short line below the 4.
- When you subtract 6-4, the answer is 2. Place this below the line. Then bring down the 55, placing it after 2.
- Here comes the most confusing part. Double the 2 in the divisor position. Place the resulting 4 a little to the left of the 255.
- What number multiplied by 4 will give a product of no more than 25? Place that number above the 55 in the quotient place AND after the 4 to the left. Multiply the digit above the 55 and the 2-digit number the the left of 255 and place it below the 255. If it be larger than 255, try one number smaller at top and to the left. In this example, the number is 5.
- The product is 225. Draw a short line below the 225.
- Subtract that number from 255. The result is 30.
- Bring down the 36, giving a figure of 3036.
- Here is another tricky spot. Multiply the 5 in 45 by 2. The answer is 10. Write down 0 to the left of 3036. Since there is 1 to carry, add it to the 4, resulting in 50.
- What number multiplied by 5 in the 50 will give 30 or a number just below 30? Try 6.
- Place 6 in the quotient position above the 36 in the dividend position AND after the 50 at the left.
- Mulltiply 6 and 506. The answer is 3056. Draw a short line below 3036
- Subtract. There is no remainder.
- Thus, this is a perfect square. The square root of 65536 is 256.
Finding the square root of 96, a non-perfect square.
Take a pencil and paper and follow the steps provided.
- Write the number as if it were the dividend of a dividing question, but place a square root sign to the left.
- What number multiplied by itself is equal to 96 or a number just below 96? It will be 9, as 9×9=81.
- Place 9 above the 9 AND in the normal place of a divisor. Multiply 9 x 9 and place 81 beneath the 96. Draw a short line below the 96.
- When you subtract 96 – 81, the answer is 15. Place this below the line. Then place a decimal point follwed by 00 after the 96. Bring down the 00, placing it after 15.
- Double the 9 in the divisor position. Place the resulting 18 a little to the left of the 1500.
- What multiplied by 18 will give the number under 150. This will involve trial and error. The best number is 7.
- Place 7 over the 00 in the dividend position and to the right of 18 on the side. Multiply 7 x 187.
- The answer is 1309. Place this beneath 1500 and subtract. The result is 191.
- Add another 00 in the dividend position. Bring it down and place it after 191.
- Follow the procedure that you have just completed.
- Be careful when you double the right hand digit on the left. It is only the 7 in 187 that is doubled. Since 2 x 7 = 14, the 1 must be carried. Thus the number at the left is 194, NOT 374.
- You will find that the number on top will be 9. Thus 9 x 1949 is 17541. Subtract 19100 – 17541. The result is 1559.
- Thus, the square root of 96 is 9.79 with a large remainder. Actually, when you round up to the nearest hundredth, the answer will be 9.80.
- If you have a calculator, find the square root of 96. The answer is 9.797958971. Rounding to the nearest hundredth, it would be 9.80.
