Question

The square root of \[350\] lies between which pair of numbers?
a) \[18{\text{ and 19}}\]
b) \[{\text{35 and 36}}\]
c) \[{\text{3}}{\text{.5 and 3}}{\text{.6}}\]
d) \[{\text{7 and 8}}\]

Answer 1

Hint: We have to find the two numbers between which the square root of \[350\] lies. As we know \[350\] is not a perfect square so, its square root will not be a natural number rather it will lie between two natural numbers. First, we will find two numbers close to \[350\] that is a perfect square and then we will take the root of those two numbers to find the required pair of numbers.

Complete answer:
On just seeing 350 one thing that comes to our mind is that it is less than \[400\]. So, its square root will be less than \[20\].
Now we know the square of \[19\] is \[361\]. Also, the square of \[18\] is \[324\].
We can see clearly that \[350\] lies between \[324{\text{ and 361}}\]. Since, \[324\] and \[361\] are the squares of \[18\] and \[19\] respectively. So, the square root of 350 lies between \[18\] and \[19\].

Therefore, the correct option is A

Note: One can also think of calculating the exact number by finding the square root but that will be time taking also there is no need of that because we are not asked the exact square root of \[350\] rather we are asked the pair of numbers between which the square root of \[350\] lies. To solve these types of questions it is better to remember the squares of numbers up to thirty. Another thing to note is that the square of any real number cannot be a negative number.