Question

6. What is the least number to be multiplied with 980 in order to get a perfect square?​

Answer 1

Answer:

980 = 2 × 490 = 2 × 2 × 245 = 2 × 2 × 5 × 4 9 = 2 × 2 × 5 × 7 × 7.

If we examine the above factorization we find that;

980 = 2² × 5¹ × 7²,

we observe that whereas the prime factors 2 and 7 occurs in pairs, the factor 5 occurs only once. The smallest number by which 980 needs to be mutiplied to make the product a perfect square is 5, which would also make factor 5 occur in a pair.

Step-by-step explanation:

A perfect square always has its prime factors in pairs of two. So writing given number 980 as its prime factors-

980=2×2×5×7×7

So obviously if we multiply it by 5 , then it will become perfect squares.

hope will be helpful ☺️

Answer 2

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We have to calculate the smallest number that is multiplied with 980 to make the product is a perfect square. Let us factorize the number 980. We will get that, 980=2×7×7×2×5. So, the only non-paired number is 5.