Find the value of the letters
A B
× A B
6 A B
Solution:
B × B = Number ending with B
B = 5 or 6
We also see from the given problem that 6AB is the square of the number AB. Since B = 5 we can write
A5 × A5 = 6A5
The square of 20 is 400 and the square 30 is 900. The square number is a three digit number starting with 6 and ending with 5.
Hence the number AB = 25
25 × 25 = 625
If B = 6
B × B = Number ending with digit B
6 × 6 = 36 which ends with digit 6
The number 6A6 has to be a square.
The value of A which makes 6A6 a square is 7 but
76 × 76 ≠ 676
Therefore A = 2 and B = 5
✦ Try This: Find the value of the letters
A B
× A B
A 9 B
B × B = Number ending with B
B = 5 or 6
If B = 5
B × B = Number ending with digit 5
A95 cannot be a perfect square ending with 5
If B = 6
A96 can be a perfect square ending with 6 if A = 1
The next three digit perfect square is 196
Hence we can see that
A = 1 and B = 4
14 × 14 = 196
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16
NCERT Exemplar Class 8 Maths Chapter 13 Problem 57
Find the value of the lettersA B × A B = 6 A B
Summary:
If A B × A B = 6 A B, then A = 2 and B = 5
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