BROWS - Time and Work.pptx

BROWS - Time and Work.pptx

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  BROWS is helpingdeprived children learn mathematics as a life skill. In support of this, BROWS is taking sessions with the help of Volunteers for the government school children / Orphan homes, to make mathematics as FUN. We expect that this will improve the IQ, Logical Skills and build their careers in long-run enable children to choose better career paths and sustainability Mathematics – as a Life Skill
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  Mathematics – as aLife Skill SQUARE ROOTS
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  Mathematics – as aLife Skill What is Square? Square roots work the opposite way of a square. For example : The square of the numbers 3 is 9, therefore the square root of number 9 is 3. Definition of Square Root The square root of a number is a value that can be multiplied by itself to give the original number. The square root of 9 is 3, because when 3 is multiplied by itself, you get 9. Decimal Numbers Decimal numbers can also be squared. And therefore you can find their square root too. For example, the square of 3.13 is 9.77 and so the square root is 3.13 The Square Root Symbol √ The square root symbol as you can see looks like a tick, and was introduced hundreds of years ago as a dot with flick upwards. So the √25 = 5
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  Mathematics – as aLife Skill TIPS AND FORMULAS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 Perfect Squares Perfect squares are squares of whole numbers. Let us look at a few perfect squares. Here is a list of squares from 1 to 15
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  Mathematics – as aLife Skill We can estimate the square root of a perfect square number using a trick. In order to determine the square root without using a long division, we must know the unit digits of squares of the first ten numbers. TRICKS TO CALCULATE SQUARE ROOT It is possible to calculate the square root of a number having 4 digits as well as 5 digits. Let us learn to calculate the square root of numbers using the trick.
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  Mathematics – as aLife Skill TRICKS TO CALCULATE SQUARE ROOT Square Root Trick for 4 Digit Numbers The steps to estimate the square root of a 4 digit number are: Step 1: Pair the digits starting from right to left. Step 2: Match the unit digit of number from the chart and determine the possible values of the square root of the unit digit. Step 3: Let us consider the first pair of digits. Let it be "n". Step 4: Determine between which two squares this number lies, √a2 < n < √b2. This concludes that a < n < b. Thus, the tens digit of the desired square root is "a". Step 5: As referred to in the chart of squares, there are only two numbers whose squares do not repeat i.e, 5 and 10. Check if the unit digit obtained in Step 2 is anyone of them. Step 6: Once, it is checked if the obtained number is 5 or 10, then they are written as it is, else we find out the unit digit by using the below steps. Steps to find units digit if the unit digit obtained in Step 2 is apart from 5 or 10 are: Step 7: Now, Multiply a and b. Step 8: If ab≤ n, then choose b, else choose a.
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  Mathematics – as aLife Skill TRICKS TO CALCULATE SQUARE ROOT Square Root Trick for 5 Digit Numbers The steps to estimate the square root of a 5 digit number are: Step 1: First pair the digits starting from right to left. Step 2: Match the unit digit of number from the chart and determine the possible values of the square root of the unit digit. Step 3: Let us consider the group of the first three digits. Let it be "n". Step 4: Determine between which two squares this number lies, √a2 < n < √b2. This concludes that a < n < b. Thus, the tens digit of the desired square root is "a". Step 5: As referred to in the chart of squares, there are only two numbers whose squares do not repeat i.e, 5 and 10. Check if the unit digit obtained in Step 2 is anyone among them. Step 6: Once, it is checked if the obtained number is 5 or 10, then they are written as it is, else we find out the unit digit by using the steps below. Steps to find units digit if the unit digit obtained in Step 2 is apart from 5 or 10 are: Step 7: Now, Multiply a and b. Step 8: If ab≤ n, then choose b, else choose a.
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  Mathematics – as aLife Skill PRACTICE PROBLEMS Q 1. Find the square root of 1521. Solution: The steps to determine the square root of 1521 are: The digits of 1521 are paired as 15 21. The unit digit of 1521 is 1. Hence, the possible unit digits, as per the chart, after taking the square root could be 1 and 9. Let us consider the pair of digits 15. The number 15 lies between two perfect squares 9 and 16 that is, 9 < 15 < 16 which can be written as 32 < 15 < 42. Hence, the tens digit of the square root of 1521 is 3 since 3 < 4. As the number obtained in step 2 is, 1 and 9. The numbers can be 31 or 39. The product of the possible tens digits gives the value 12 (as here a = 3 and b = 4). As 12 < 15, the square root of 1521 will be the greater of 31 and 39 which is 39.
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  Mathematics – as aLife Skill PRACTICE PROBLEMS Q 2. Find the square root of 6241 Solution: The steps to determine the square root of 6241 are: The digits of 6241 are paired as 62 41. The unit digit of 6241 is 1. Hence, the possible unit digits after taking square root could be 1 and 9. When we consider the first two digits of 6241, that are 62. The number 62 lies between 7 and 8 that is, 49 < 15 < 64 which can be written as 72 < 15 < 82. Hence, the tens digit of the square root of 6241 is 7. As the number obtained in step 2 is, 1 and 9. The numbers can be 71 or 79. In order to determine the square root of 6241, we multiply the tens and one's digits in both cases. 62 lies between 72 and 82. Their product gives the value 56. As 56 < 62, the square root of 6241 will be greater than 71 and 79 which is 79. Thus, the square root of 6241 is 79.
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  Mathematics – as aLife Skill PRACTICE PROBLEMS Q 3. Find the square root of 10816. Solution: The steps to determine the square root of 10816 are: The digits of 10816 are paired as 108 16. The unit digit of 10816 is 6. Hence, the possible unit digits after taking square root could be 4 and 6. When we consider the first three digits of 10816, that are 108. The number 108 lies between two perfect squares 100 and 121 that is, 100 < 108 < 121 which can be written as 102 < 108 < 112. Hence, the tens digit of the square root of 10816 is 10 as 10 < 11. As the number obtained in step 2 is, 4 and 6. The numbers can be 104 or 106. 108 lies between 102 and 112. Their product gives the value 110. As the 110 > 108, the square root of 10816 will be the lesser of 104 and 106 which is 104.
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  Mathematics – as aLife Skill PRACTICE PROBLEMS Q 4. Calculate the square root of 24649 Solution:The steps to determine the square root of 24649 are: The digits of 24649 are paired as 246 49. The unit digit of 24649 is 9. Hence, the possible unit digits after taking square root could be 3 and 7. When we consider the first two digits of 24649, that are 246. The number 246 lies between 225 and 256 that is, 225 < 246 < 256 which can be written as 152 < 246 < 162. Hence, the tens digit of the square root of 24649 is 15. As the number obtained in step 2 is, 3 and 7. The numbers can be 153 or 157. In order to determine the square root of 24649, we multiply the tens and one's digits in both cases. 246 lies between 152 and 162. Their product gives the value 240. As 240 < 246, the square root of 10816 will be greater than 153 and 157 which is 157. Thus, the square root of 24649 is 157.
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  Mathematics – as aLife Skill ASSESSMENT Q1. Calculate the square root of 4,225 ? Answer – 65 Q2. Calculate the square root of 25,281 ? Answer – 159 Q3. Calculate the square root of 5,329 ? Answer – 73 Q4. Calculate the square root of 14,884? Answer – 122 Q5. Calculate the square root of 30,625 ? Answer – 175
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  Mathematics – as aLife Skill REFERENCES 1. https://www.cuemath.com/algebra/square-root-tricks/ 2. https://www.vedantu.com/maths/square-root-tricks
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  Happy Learning -Thank you Mathematics – as a Life Skill