Question

Find the least number which must be added to 9050 to make it a perfect square​

Answer 1

Required Answer:-

Step 1 : Firstly we have to divide 9050 by using long division method. Refer to the attached image for calculations.

So, after solving we got Quotient's value as 95.

Step 2 : Compare the √9050 by the actual Quotient and actual Quotient + 1 (Increased number) which is 96.

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$\dashrightarrow \sf \: \: 95 < \: \bf\sqrt{9050} \: \: > \sf 96$

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Step 3 : Now, we will make the square of 96 and will perform subtraction between 96² and 9050.

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$\dashrightarrow \: \: \sf \: (96)^2 - 9050$

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$\dashrightarrow \: \: \: \sf 9216 - 9050$

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$\dashrightarrow \: \: \: \underline{\large{ \boxed{ \tt{ \green{\pmb{166}}}}}}$

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$\therefore$ 166 must be added to 9050 to make it a perfect square.

Step 4 : For checking your answer, add 166 to 9050 and then take out the square root of the result obtained.

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$\dashrightarrow \: \: \: \sf 9050 + 166 = 9216$

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$\dashrightarrow \: \: \: \sf \sqrt{9216} = 96$

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$\dashrightarrow \: \: \: \sf (96)^2 = 9216$

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Final Answer :

➛ 166 must be added to 9050 to make it a perfect square.

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More to know :-

• In such types of questions when subtraction and addition is there, we need to apply long division method.

• And in multiplication and division, we shall apply prime factorisation method.