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Page 1 3. Squares and Square Roots EXERCISE 3(A) Question 1. Find the square of : (i) 59 (ii) 63 (iii) 15 Solution: (i) Square of 59= 59 x 59 = 3481 (ii) Square of 6.3 = 6.3 x 6.3 = 39.69 (iii) Square of 15 = 15 x 15 = 225 Question 2. By splitting into prime factors, find the square root of : (i) 11025 (if) 396900 (iii) 194481 Solution: Page 2 3. Squares and Square Roots EXERCISE 3(A) Question 1. Find the square of : (i) 59 (ii) 63 (iii) 15 Solution: (i) Square of 59= 59 x 59 = 3481 (ii) Square of 6.3 = 6.3 x 6.3 = 39.69 (iii) Square of 15 = 15 x 15 = 225 Question 2. By splitting into prime factors, find the square root of : (i) 11025 (if) 396900 (iii) 194481 Solution: Question 3. (i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square. (ii) Find the smallest number by which 12748 be mutliplied so that the product is a perfect square? Solution: On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor. The given number should be multiplied by 2 to make the given number a perfect square. On grouping the prime factors of 12748 as shown; one factor i.e. 3187 is left which cannot be paired with equal factor. Page 3 3. Squares and Square Roots EXERCISE 3(A) Question 1. Find the square of : (i) 59 (ii) 63 (iii) 15 Solution: (i) Square of 59= 59 x 59 = 3481 (ii) Square of 6.3 = 6.3 x 6.3 = 39.69 (iii) Square of 15 = 15 x 15 = 225 Question 2. By splitting into prime factors, find the square root of : (i) 11025 (if) 396900 (iii) 194481 Solution: Question 3. (i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square. (ii) Find the smallest number by which 12748 be mutliplied so that the product is a perfect square? Solution: On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor. The given number should be multiplied by 2 to make the given number a perfect square. On grouping the prime factors of 12748 as shown; one factor i.e. 3187 is left which cannot be paired with equal factor. The given number should be multiplied by 3187. Question 4. Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers. Solution: Question 5. Find the square root of : (i) 0.1764 Page 4 3. Squares and Square Roots EXERCISE 3(A) Question 1. Find the square of : (i) 59 (ii) 63 (iii) 15 Solution: (i) Square of 59= 59 x 59 = 3481 (ii) Square of 6.3 = 6.3 x 6.3 = 39.69 (iii) Square of 15 = 15 x 15 = 225 Question 2. By splitting into prime factors, find the square root of : (i) 11025 (if) 396900 (iii) 194481 Solution: Question 3. (i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square. (ii) Find the smallest number by which 12748 be mutliplied so that the product is a perfect square? Solution: On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor. The given number should be multiplied by 2 to make the given number a perfect square. On grouping the prime factors of 12748 as shown; one factor i.e. 3187 is left which cannot be paired with equal factor. The given number should be multiplied by 3187. Question 4. Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers. Solution: Question 5. Find the square root of : (i) 0.1764 (ii) (iii) 0.0169 Solution: Question 6. Evaluate Solution: Page 5 3. Squares and Square Roots EXERCISE 3(A) Question 1. Find the square of : (i) 59 (ii) 63 (iii) 15 Solution: (i) Square of 59= 59 x 59 = 3481 (ii) Square of 6.3 = 6.3 x 6.3 = 39.69 (iii) Square of 15 = 15 x 15 = 225 Question 2. By splitting into prime factors, find the square root of : (i) 11025 (if) 396900 (iii) 194481 Solution: Question 3. (i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square. (ii) Find the smallest number by which 12748 be mutliplied so that the product is a perfect square? Solution: On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor. The given number should be multiplied by 2 to make the given number a perfect square. On grouping the prime factors of 12748 as shown; one factor i.e. 3187 is left which cannot be paired with equal factor. The given number should be multiplied by 3187. Question 4. Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers. Solution: Question 5. Find the square root of : (i) 0.1764 (ii) (iii) 0.0169 Solution: Question 6. Evaluate Solution:Read More
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