Question

2. Find the squares of the following numbers using the Diagonal method.Verify the result by finding the square using the prime factorisation method :
(i) 89​

Answer 1

Step-by-step explanation:

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7921

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Step1: 89 = 2digit so we will make a square 2 by 2 and make 4 sub square in it and draw diagonal in each sub square ( U can see picture for more detail)

Step2: write 8 and 9 vertically and horizontally

8×8 = 64 ( 1st sub square)

Write tens place in upper triangle and one place in lower triangle

8×9 = 72 (2nd sub square)

Write tens "7" place in upper triangle and "2" one place in lower triangle

8×9 = 72 ( 3rd sub square)

Write tens "7" place in upper triangle and "2" one place in lower triangle

9×9 = 81 (4th sub square)

Write tens "8" place in upper triangle and "1" one place in lower triangle

Step 3:Now we will take all elements diagonally

1st we will take 1 because this diagonal has only 1 element

( 1) = 1

Step 4: (2+8+2) = 12 = take right side which is 2 left side will add in next step " as carry"

Step 5: (7+4+7+1) = 19 = Take right side which is

9 and left side will add in next step

Step 6: (6+1) = 7

combine all digits: 7 9 2 1

Verify by prime factorization:

89| 7921

89| 89

| 1

Prime factors of 7921: 89×89

7921 = 89²

sqrt of 7921 = 89

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