Complete the following table S. No. Number Prime Factors Smallest number to be multiplied to make the given number a perfect square (i) 2700 2 × 2 × 3 × 3 × 3 × 5 × 5 3 , 2700 × 3 = 8100 (ii) 1575 --------- ---------- (iii) 1620 --------- ---------- (iv) 11200 --------- ----------

(ii) The given number is 1575 The prime factorisation of 1575 is, 3 1575 3 525 5 175 5 35 7 Therefore, 1575 = 3 × 3 × 5 × 5 × 7 As the prime factor 7 has no pair, 1575 is not a perfect square. So, we multiply 1575 by 7 to get a perfect square. Therefore, 1575 × 7 = 11025 is a perfect square. (iii) The given number is 1620 The prime factorisation of 1620 is, 2 1620 2 810 3 405 3 135 3 45 3 15 5 Therefore, 1620 = 2 × 2 × 3 × 3 × 3 × 3 × 5 As the prime factor 5 has no pair, 1620 is not a perfect square. So, we multiply 1620 by 5 to get a perfect square. Therefore, 1620 × 5 = 8100 is a perfect square. (iv) The given number is 11200 The prime factorisation of 11200 is, 2 11200 2 5600 2 2800 2 1400 2 700 2 350 5 175 5 35 7 Therefore, 11200 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 7 As the prime factor 7 has no pair, 11200 is not a perfect square. So, we multiply 11200 by 7 to get a perfect square. Therefore, 11200 × 7 = 78400 is a perfect square. Hence, the table is S. No. Number Prime Factors Smallest number to be multiplied to make the given number a perfect square (i) 2700 2 × 2 × 3 × 3 × 3 × 5 × 5 3 , 2700 × 3 = 8100 (ii) 1575 3 × 3 × 5 × 5 × 7 7 , 1575 × 7 = 11025 (iii) 1620 2 × 2 × 3 × 3 × 3 × 3 × 5 5 , 1620 × 5 = 8100 (iv) 11200 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 7 7 , 11200 × 7 = 78400

Complete the following table S. No. Number Prime Factors Smallest number by which number should be divided to make a perfect square (i) 2700 2 × 2 × 3 × 3 × 3 × 5 × 5 3 , 2700 ÷ 3 = 900 (ii) 1620 --------- ---------- (iii) 14175 --------- ---------- (iv) 25857 --------- ----------

(ii) The given number is 1620 The prime factorisation of 1620 is, 2 1620 2 810 3 405 3 135 3 45 3 15 5 Therefore, 1620 = 2 × 2 × 3 × 3 × 3 × 3 × 5 As the prime factor 5 has no pair, 1620 is not a perfect square. So, we divide 1620 by 5 to get a perfect square. Therefore, 1620 ÷ 5 = 324 is a perfect square. (iii) The given number is 14175 The prime factorisation of 14175 is, 3 14175 3 4725 3 1575 3 525 5 175 5 35 7 Therefore, 14175 = 3 × 3 × 3 × 3 × 5 × 5 × 7 As the prime factor 7 has no pair, 14175 is not a perfect square. So, we divide 14175 by 7 to get a perfect square. Therefore, 14175 ÷ 7 = 2025 is a perfect square. (iv) The given number is 25857 The prime factorisation of 25857 is, 3 25857 3 8619 13 2873 13 221 17 Therefore, 25857 = 3 × 3 × 13 × 13 × 17 As the prime factor 17 has no pair, 25857 is not a perfect square. So, we divide 25857 by 17 to get a perfect square. Therefore, 25857 ÷ 17 = 1521 is a perfect square. Hence, the table is S. No. Number Prime Factors Smallest number to be multiplied to make the given number a perfect square (i) 2700 2 × 2 × 3 × 3 × 3 × 5 × 5 3 , 2700 ÷ 3 = 900 (ii) 1620 2 × 2 × 3 × 3 × 3 × 3 × 5 5 , 1620 ÷ 5 = 324 (iii) 14175 3 × 3 × 3 × 3 × 5 × 5 × 7 7 , 14175 ÷ 7 = 2025 (iv) 25857 3 × 3 × 13 × 13 × 17 17 , 25857 ÷ 17 = 1521

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Important Questions on Squares and Square Roots

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 5

Find the square root of the following number by prime factorization method.

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 5

Find the square root of the following number by prime factorization method.

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 5

Find the square root of the following number by prime factorization method.

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 6

Complete the following table

S. No.	Number	Prime Factors	Smallest number to be multiplied to make the given number a perfect square
(i)	$2700$	$2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5$	$3, [2700 \times 3 = 8100]$
(ii)	$1575$	---------	----------
(iii)	$1620$	---------	----------
(iv)	$11200$	---------	----------

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 6

Complete the following table

S. No.	Number	Prime Factors	Smallest number by which number should be divided to make a perfect square
(i)	$2700$	$2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5$	$3, [2700 \div 3 = 900]$
(ii)	$1620$	---------	----------
(iii)	$14175$	---------	----------
(iv)	$25857$	---------	----------

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 7

Find the least number which must be subtracted from the following number so as to get a perfect square. Also, find the square root of the perfect square so obtained.

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 7

Find the least number which must be subtracted from the following number so as to get a perfect square. Also, find the square root of the perfect square so obtained.

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NCERT Practice Workbook Mathematics>Chapter 6 - Squares and Square Roots>Worksheet 2>Q 7

Find the least number which must be subtracted from the following number so as to get a perfect square. Also, find the square root of the perfect square so obtained.

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Important Questions on Squares and Square Roots

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