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High School Mathematics
2.6 Problems on Square Roots - I

Example:
Find the least number, that should 20480 be multiplied or divided so that it becomes perfect square.
Solution:
Take the prime factors of the given number.
20480 = 2 * 10240
= 2 * 2 * 5120
= 2 * 2 * 2 * 2560
= 2 * 2 * 2 * 2 * 1280
= 2 * 2 * 2 * 2 * 2 * 640
= 2 * 2 * 2 * 2 * 2 * 2 * 320
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 160
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 80
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 40
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 20
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 10
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5
In the product there are 12 twos and only one 5, to make the product into group of equal factors one more 5 is required. So the number 20480 is to be multiplied or divided by 5 to make it a perfect square.

Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: With what least number should 1792 be multiplied or divided so that it becomes perfect square.
5
3
9
7

Q 2: With what least number should 2187 be multiplied or divided so that it becomes perfect square.
3
7
5
9

Q 3: With what least number should 4375 be multiplied or divided so that it becomes perfect square.
5
9
7
3

Q 4: With what least number should 6480 be multiplied or divided so that it becomes perfect square.
6
8
5
3

Q 5: With what least number should 1875 be multiplied or divided so that it becomes perfect square.
5
9
3
7

Q 6: With what least number should 13122 be multiplied or divided so that it becomes perfect square.
2
3
5
7

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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