Question

What perfect square goes into 150?

Answer 1

Hint: We are asked to find which square root goes into the given number. To find this, we need to find the factors of the given number 150 and check if any of them are perfect squares and then we can find which perfect square number goes into it.

Complete step by step solution:
The number for which we need to find a perfect square inside, given in the question is 150, so we are asked to find the perfect squares among the factors of 150.
Next, we can write 150 in terms of its factors as,
$150=50\times 3$
Hence 3 and 50 are factors. Also, we can write it as,
$150=30\times 5$
Hence 5 and 30 are factors. Next, we can write it as,
$150=25\times 6$
Hence 25 and 6 are factors. Next, we can write it as,
$150=15\times 10$
Hence 15 and 10 are factors. Next, we can write it as,
$150=75\times 2$
Hence 75 and 2 are factors. Next, we can write it as,
$150=150\times 1$
Hence 150 and 1 are factors.
The list of all factors of 150 are 1,2,3,5,6,10,15,25,30,50,75 and 150. Therefore, the perfect square among this is 25 and this is the required result.

Note: While finding the factors, we can speed up the process by examining which number may be multiplied more than once in the given number. We can clearly see that 150 is divisible by 5 twice and hence 25 is the perfect square in 150.