Put three different numbers in the circles so that when you add the numbers at the end of each line you always get a perfect square.
Solution:
Put three different numbers in the circles.
On adding the numbers at the end of each line we get a perfect square.
A natural number is called a perfect square if it is the square of some natural number.
i.e., if m = n², then m is a perfect square where m and n are natural numbers.
Let us fill one circle with the number 6
Fill the next circle with the number 19
Adding both, 6 + 19 = 25
Square of 5 = 25
Therefore, 25 is a perfect square.
Fill the third circle with the number 30
On adding, 19 + 30 = 49
Square of 7 = 49
Therefore, 49 is a perfect square.
Now add 6 + 30 = 36
Square of 6 = 36
Therefore, 36 is a perfect square.
Therefore, the required numbers are 6, 19 and 30.
✦ Try This: Find the least number which must be added to 984 to make it a perfect square. Also, find the square root of the perfect square number so obtained.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 139
Put three different numbers in the circles so that when you add the numbers at the end of each line you always get a perfect square
Summary:
The three different numbers to be put in the circles so that when you add the numbers at the end of each line you always get a perfect square are 6, 19 and 30.
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