Question

7. What is the smallest natural number by which 22050 should be multiplied so that the
resulting natural number will be perfect square?​

Answer 1

Answer:

hope this answer help you

Answer 2

Final answer: Smallest number by which 22050 must be multiplied so that the product is a perfect square is 2.    

Given that: We are given 22050.

To find: We have to find smallest number by which 22050 must be multiplied so that the product is a perfect square.

Explanation:

• To find the smallest natural number by which 22050 should multiplied so that the resulting natural number will be perfect square, first find the factor of the given number 22050.

• 22050 expressed as,

22050 = 2 * 11025

           = 2 * 3 * 3675

           = 2 * 3 * 3 * 1225

           = 2 * 3 * 3 * 5 * 245

           = 2 *  3 * 3 * 3 * 5 * 5 * 49

           = 2 * 3 * 3 * 5 * 5 * 7 * 7

so, 22050 = 2 * 3 * 3 * 3 * 5 * 5 * 7 * 7

                  = 2 *(3² * 5² * 7²)

• Here we can see that 2 does not appear in pairs. 2 is left unpaired. To make 22050 a perfect square we need one more 2.  So we will multiply 22050 by 2,

22050 * 2 = 44100

44100 = 210 * 210

• Hence smallest number by which 22050 must be multiplied so that the product is a perfect square is 2.

To know more about the concept please go through the links

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