# 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

**☛ Related Questions:**

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