Question

How do you find the perfect square between 60 and 70?

Answer 1

Hint: We need to know the definition of square number. A square number is defined as numbers that are multiplied by itself. For example 4 is a square number (perfect square) because 2 Is multiplied by itself to give us 4. To solve this easily we need to know the square of the numbers starting from 1 to 10. 

Complete step-by-step answer:

Before finding the perfect square between 60 and 70. Let’s find the square numbers up to 10.

 \[{1^2} \to 1 \times 1 = 1\] 

 \[{2^2} \to 2 \times 2 = 4\] 

 \[{3^2} \to 3 \times 3 = 9\] 

 \[{4^2} \to 4 \times 4 = 16\] 

 \[{5^2} \to 5 \times 5 = 25\] 

 \[{6^2} \to 6 \times 6 = 36\] 

 \[{7^2} \to 7 \times 7 = 49\] 

 \[{8^2} \to 8 \times 8 = 64\] 

 \[{9^2} \to 9 \times 9 = 81\] 

 \[{10^2} \to 10 \times 10 = 100\] .

They asked us to find the perfect square between 60 and 70.

We can see that 64 is the only perfect square between 60 and 70.

Hence, the required answer is 64.

                                      (OR) 

Another definition of a perfect square is, a number is said to be a perfect square number if and only if the prime factor of a number is grouped in a pair of equal factors.

The factors of 64 are 2 multiplied six times.

That is   \[64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2\] 

 \[ = (2 \times 2) \times (2 \times 2) \times (2 \times 2)\] 

 \[ = {2^2} \times {2^2} \times {2^2}\] 

 \[ = {\left( {2 \times 2 \times 2} \right)^2}\] 

 \[64 = {8^2}\] 

So, the correct answer is “ 64.”

Note: Remember that a number that has 2, 3, 7, or 8 at its unit’s place can never be a perfect square. The square root of a number is a value that we get when it is multiplied by itself and produces the original number. For example, 8 is multiplied by itself we get 64. Thus we can say that 8 is a square root value of 64. We also know that square and square root will cancel out.