Chapter 8.4, Problem 3P

(a)

To determine

To find:To solve expression 85² using mental maths.

Answer to Problem 3P

  ${85}^2=7225$

Explanation of Solution

Given information:

The expression 85²

Calculation:

As the last digit of number is 5

So the square will end by 25

For finding first digit

Multiply 8 with its consecutive digit i.e. 9

  $8\times 9=72$

So the answer is 7225

Conclusion:

  ${85}^2=7225$

(b)

To determine

To find:To provide other method for finding 85² by mental maths.

Answer to Problem 3P

The answer is ${85}^2=7225$

Explanation of Solution

Given information:

85²

Calculation:

The number for multiplication are 85 and 85.

So firstly we draw slant lines for both the digits and lines of other digit will be opposite in direction.

  

Now count the intersection point and write it as ABC

In C the number is 25 so carry 2 in next section C=5

In B the intersection points are $40+40+2=82$ so 8 will carry on the value of A

B=2

In A the intersection points are $64+8=72$ so the value of A is 72

So the answer is ${85}^2=7225$

Conclusion:

The answer is ${85}^2=7225$