This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Finding the Square of a Number”.
1. What can be general formula to find square of any number?
Explanation: The general formula of finding square of any number is (a±b)2. Option a2 cannot be correct because if we need to find square of number such as 23 the method using the general formula (a±b)2 would be more easier. Hence the correct option is (a±b)2.
2. How can one represent the square of 103?
Explanation: The number 103 can be represented in form 100+3, this will help us to calculate the square of the number. This method would help us eliminate the traditional method of multiplying the number with itself.
3. 892= ____
Explanation: If we have to find the square of the number which is near 0 we use the second variation i.e. (90-1)2. This would help us and make the calculations easier.
Therefore (90-1)2= 902-2×90×1+12
Therefore (90-1)2= 8100-180+1
4. If a student uses (a-b)2 to calculate the square of a number, then the number is _______
Explanation: A student uses this variant of the formula for the numbers which are near 0. Here there is only one number which is close to 0 and hence 199 is the correct answer. The other options also can be solved using this method but that would be complicated.
5. Calculate the square of 201.
Explanation: In the multiple choice question student can eliminate three options by mere observation. The student should notice that option 41042 contains 2 in its unit place so it cannot be a square of number ending with 1. Similarly, the other two options 39393 & 40426 ending with 3 and 6 whereas square of numbers ending with 1 have only 1 in its unit place.
Explanation: In order to calculate the square of 34 we use the formula,
(a+b)2, where we consider a=30 and b=4
Therefore (30+4)2 = 302+2×30×4+42
Therefore (30+4)2 = 900+240+16
Therefore (30+4)2 = 1156.
7. How many numbers lie between the squares of 12 and 13?
Explanation: If we need to find the number of non-square numbers, we can use the formula (2n+1).
Here when we apply this formula we get, (2×12+1)=25. Hence the answer would be 25 and the other options would be incorrect.
8. Express the square of 11 in terms of sum of odd numbers.
Explanation: The correct option is the one with the first 11 odd numbers as the sum of first n odd numbers gives n2. Hence the correct answer is the one with the first 11 odd number.
9. Find the square of 25.
Explanation: There is a beautiful pattern followed by all the numbers ending with 5. We can get the square of any number ending with 5 without actually calculating it. All the numbers ending with 5 shows 25 at the end of their squares, and the other places can be filled by multiplying the next consecutive number. For example: 252 = (2×3)25 i.e.625 (the step shown is just for understanding).
10. Find the square of 225.
Explanation: There is a beautiful pattern followed by all the numbers ending with 5. We can get the square of any number ending with 5 without actually calculating it. All the numbers ending with 5 shows 25 at the end of their squares, and the other places can be filled by multiplying the next consecutive number. For example: 2252 = (22×23)25 i.e.50625 (the step shown is just for understanding).
Sanfoundry Global Education & Learning Series – Mathematics – Class 8.
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