What smallest number should 240 be multiplied to get a perfect square number?
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The following steps will be useful to find the least number which has to multiplied by the given number to get a perfect square. Show 1. Decompose the given numbers into its prime factors. 2. Write the prime factors as pairs such that each pair has two same prime factors. 3. Find the prime factor which does not occur in pair. That is the least number to be multiplied by the given number to get a perfect square. Here we are asked to find the smallest number which must be multiplied to 240 to make it a perfect square . So , lets do prime factorisation of 240 . Here , 240 = 2 × 120 . = 2 × 2 × 60. = 2 × 2 × 2 × 30. = 2 × 2 × 2 × 2 × 3 × 5 . Hence we got 240 = 2⁴ × 3¹ × 5¹ . Now here we can see that , in order to make a perfect square it should be multiplied by 3 × 5 = 15 in order to make power of prime factors even . What is the smallest whole number 24 could be multiplied by to make it a square number?The smallest number by which 24 should be multiplied to make it a perfect square? Therefore the least number by which 24 should be multiplied is 6.
What is the least number to be multiplied to get a perfect square?So, '5' is the least number to be multiplied by 180 to get a perfect square.
What is the perfect square of 240?Square Root of 240 Solved Examples
The perfect squares nearest to 240 are 225 and 256.
What smallest number should be added to 250 to make it a perfect square?Answer. For 2 to be a perfect square , the power of prime factors to be even . Hence , 250 Should be multiplied with 2 × 5 to make a perfect square . Therefore , the smallest number by which 250 can be multiplied to get a perfect square is 10 .
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