Question

Q.52 Find the greatest number
of 5 digits which is a perfect
square - Also find its square
root. (5)or Find the values of
395x395 - 205 x 205/600
using identities. please answer
​

Answer 1

PLEASE REFER THE ATTACHED IMAGE AS IT IS SAVING THE DIVISION METHOD AS REQUIRED,

We know that largest 5 digit number is 99999

By using division method

316

- - - - - - - -

3 99999

+3 - 9

------- - - - - - - - - -

61 99

+1 - 61

------- - - - - - - - - - -

626 3899

- 3756

- - - - - - - - - - -

143

It leaves a remainder 143,hence it is not perfect square

99999 - 143 = 99856 is a perfect square

And square of 99856 = 316

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$\frac{395 \times 395 - 205 \times 205}{600} \\ = \frac{ {395}^{2} - {205}^{2} }{600} \\ = \frac{(395 + 205)(395 - 205)}{600} \\ = \frac{600 \times 190}{600} \\ = 190$