easy trick in maths for kids
Answers
Squaring a number that ends in 5
Example: 75^2
To begin, note that when you square any number that ends in 5, the last two digits of the product are 25.
Now, multiply the number in front of the 5 by the next higher number. Using 75 as an example, the number in front of the 5 is 7; multiply 7 by 8 = 56.
As an alternative method of this step, square the number in front of the 5, then add the number to the product. In this case, 7^2 + 7 = 49 + 7 = 56. If we look at the number in front of the 5 as x, then (x)(x+1) is the same as x^2 + x
Now tack 25 to the end of the number in the previous step: 75^2 = 5625.
Why it works: (a + b)^2 = a^2 + 2ab + b^2. In our example, we can say that 75 = 70 + 5. When we square this, we get 4900 + (2)(5)(70) + 25.
For another example, 85 squared = 80^2 + (10)(80) + 25 = 6400 + 800 + 25, or 7225.
What I actually do: consider the number of interest (75) to consist of two parts: the number to the left of the 5, and 5. In the case of 75, the two parts are 7 and 5. I ignore the 5 for now. I multiply the left side (7) by the next higher number (8) to get 56. Now I just tack 25 to the end of 56: the result is 5625.
This works for more than two digits; really for a number of any size. For example, look at 305. The two parts are 30 and 5. Now 30 x 31 = 925; also, using the alternative method, 30 squared + 30 = 900 + 30 = 930. Now tack the 25 onto the end to get 93025.
Squaring a number near 50
Example: 48^2
In this case, note that 48 = 50 - 2. 50 x 50 = 2500, so the answer will be a bit above or below 2500. Multiply the difference by 100, and either add it to 2500 or subtract it from 2500, depending on whether the number is above or below 50. In our example, the answer will be approximately 200 less than 2500.
To finish it, add the square of the difference to the result of the previous operation: 2300 + 2 squared = 2300 + 4 = 2304.
Why it works: (a + b) squared = a squared + 2ab + b squared; also,(a-b)squared = a squared - 2ab + b squared. For this trick, we will use 53 squared as an example. 53 squared = (50 + 3) squared = 2500 + (2)(50)(3) + 9 = 2500 + 300 + 9 = 2809.
Answer:
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