Q. 2 B5.0( 1 Vote )
Given below is a method to calculate 372?
Explain why this is correct, using algebra.
Answer :
Now lets try to understand this method using algebra.
We know that we can express any 2 digit number as 10m+n , where m is the digit at tens place and n is the digit at ones place.
Now we have to find its square, i.e. (10m + n)2
(10m + n)2 = (10m)2 + 2× 10m× n + n2 ……….using, (x+y)2 = x2 + 2xy + y2
=( m2 × 100) + ( 2mn× 10 )+ (n2 )
Now, carefully observe the above method, you will see that we were finding these terms only and then addition of these terms gives us the required square.
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Now compute the squares of these numbers in head:
10.2
Kerala Board Mathematics Part IProve that for any natural number ending in 3, its square ends in 9. What about numbers ending in 5? And numbers ending in 4?
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Check this for some more two-digit numbers.
Kerala Board Mathematics Part IIs there a general method to compute the squares of numbers like 
Explain it using algebra.
Explain using algebra, the fact that the square of any natural number which is not a multiple of 3, leaves remainder 1 on division by 3.
Kerala Board Mathematics Part ILook at this pattern
12 + (4 × 2) = 32
22 + (4 × 3) = 42
32 + (4 × 4) = 52
i) Write the next two lines.
ii) Explain the general principle using algebra.
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Find an easy method to compute squares of number ending in 5.
Kerala Board Mathematics Part ILook at this pattern
12 + (4 × 2) = 32
22 + (4 × 3) = 42
32 + (4 × 4) = 52
i) Write the next two lines.
ii) Explain the general principle using algebra.
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Find an easy method to compute squares of number ending in 5.
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Explain why this is correct, using algebra.
Kerala Board Mathematics Part I