Ex 6.3, 5 For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 Prime factorizing 252 By prime factorization, 252 = 2 × 2 × 3 × 3 × 7 Since 7 does not occur in pair, we multiply by 7 to make it a pair So, our number becomes 252 × 7 = 2 × 2 × 3 × 3 × 7 × 7 1764 = 2 × 2 × 3 × 3 × 7 × 7 Square root of 1764 ∴ √1764 = 2 × 3 × 7 = 2 × 21 = 42 ∴ The smallest whole number to be multiplied = 7 and square root of new number = 42 Show
Solution: (i) 243 Prime factors of 243 = Here 3 do not appear in 3’s group. Therefore, 243 must be multiplied by 3 to make it a perfect cube.  (ii) 256 Prime factors of 256 = 2\times2\times2\times2\times2\times2\times2\times2 Here one factor 2 is required to make a 3’s group. Therefore, 256 must be multiplied by 2 to make it a perfect cube. (iii) 72 Prime factors of 72 = 2\times2\times2\times3\times3 Here 3 does not appear in 3’s group. Therefore, 72 must be multiplied by 3 to make it a perfect cube. (iv) 675 Prime factors of 675 = 3\times3\times3\times5\times5 Here factor 5 does not appear in 3’s group. Therefore 675 must be multiplied by 3 to make it a perfect cube. (v) 100 Prime factors of 100 = 2\times2\times5\times5 Here factor 2 and 5 both do not appear in 3’s group. Therefore 100 must be multiplied by 2\times5= 10 to make it a perfect cube. Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square. \therefore252\times7=1764 And (i) \sqrt{1764}=2\times3\times7=42 (ii) 180 = 2 x 2 x 3 x 3 x 5 Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square. \therefore180\times5=900 And \sqrt{900}=2\times3\times5=30 (iii) 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7 Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square. \therefore1008\times7=7056 And \sqrt{7056}=2\times2\times3\times7=84 (iv) 2028 = 2 x 2 x 3 x 13 x 13 Here, prime factor 3 has no pair. Therefore 2028 must be multiplied by 3 to make it a perfect square. \therefore2028\times3=6084 And \sqrt{6084}=2\times2\times3\times3\times13\times13=78 (v) 1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3 Here, prime factor 2 has no pair. Therefore 1458 must be multiplied by 2 to make it a perfect square. The following steps will be useful to find the least number which has to multiplied by the given number to get a perfect square. 1. Decompose the given numbers into its prime factors. 2. Write the prime factors as pairs such that each pair has two same prime factors. 3. Find the prime factor which does not occur in pair. That is the least number to be multiplied by the given number to get a perfect square. To find a square root of a number without a calculator, see if you can get to that whole number by squaring smaller numbers, or multiplying a smaller number by itself. If the number is a perfect square, you will get a whole number as the square root. Otherwise, try squaring numbers with a decimal until you get as close as possible to your original number. If you want to learn how to estimate the square root of imperfect squares, keep reading the article! Did this summary help you?YesNo Thanks to all authors for creating a page that has been read 583,522 times.
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Home Books Audiobooks Documents What is the perfect square of 242?It is the positive solution of the equation x2 = 242. We can express the square root of 242 in its lowest radical form as 11 √2.
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Square Root of 242.. What number should be multiplied to 252 to get a perfect square?Therefore 252 must be multiplied by 7 to make it a perfect square.
What is the smallest number that should multiply 4200 to make it a perfect square?Answer. So to make 4200 a perfect square we have to divide it by 42,as 42 is the only number which is not paired.
Does 252 make a perfect square?False. 252 is not a perfect square number.
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