Find the smallest number by which 540 must be multiplied to get a perfect square. Also,
find the square root of the perfect square so obtained.
Answers
Answer:
15,90
Step-by-step explanation:
Divide 540 by prime factorisation
√540=2x2x3x3x3x5 = 3x5
=15
Multiply 2x2x3x3=6&15
Therefore, perfect square root for the perfect square obtained is 90
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The smallest number by which 540 must be multiplied to get a perfect square is 15 and the resultant square number is 8100.
Given:
Number 540
To find:
The smallest number by which 540 must be multiplied to get a perfect square.
Solution:
A perfect square number:
- A perfect square is a positive integer which is obtained by multiplying a number by itself.
- A perfect square number can be written in the form of a²
- For example, 4 = 2², 16 = 4², 100 = 10².
Given number 540
To find the required number write the given number as product of its prime factors
⇒ 540 = 2 × 2 × 3 × 3 × 3 × 5
Now group the numbers as squares
⇒ 2² × 3² × 3 × 5
After grouping the numbers 3 and 5 left
So to make 3 and 5 as squares we need add one 3 and one 5
Therefore, the number which we need to multiply is 3×5 = 15
And the resultant square number = 540 × 15 = 8100
⇒ 8100 = 90²
The smallest number by which 540 must be multiplied to get a perfect square is 15 and the obtained square number is 8100.
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