Question

find the square root by
factor method
7569​

Answer 1

Sorry my handwriting is quite bad.....I Hope your problem will be solved!!

Answer 2

Answer:

The answer is either 83 or 87

Step-by-step explanation:

Assuming that we are seeking an integer answer, then:

Step 1: If the number of digits is odd, add a ‘0’ to the start of the number - eg 743 becomes 0743. As our number is 7569, which has four digits, we don’t add the ‘0’.

Step 2: Looking at the first pair of digits, ‘75’, what is the largest digit when squared that does not exceed this pair? The answer is clearly ‘8’.

We now know that the answer is in the range (80,90)

Step 3: Look at the last digit, ‘9’. This can only occur if the last digit of the integer answer is a ‘3’ or a ‘7’ - see below.

So the answer is either ‘83’ or ‘87’. Given that ‘7569’ is clearly much nearer to ‘8100’ (=90^2) than it is to ‘6400’ (=80^2) we can conclude that the answer is ‘87’

872=(80+7)2=802+2×80×7+72=6400+1120+49=7569