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Square Root of 64
64 is a perfect square number which can be obtained by the square of 8. Hence, the square root of 64 is a rational number. In this minilesson, we will learn to find the square root of 64 along with solved examples. Let us see what the square root of 64 is.
 Square Root of 64: √64 = 8
 Square of 64: 64^{2} = 4096
1.  What Is the Square Root of 64? 
2.  Is Square Root of 64 Rational or Irrational?? 
3.  How to Find the Square Root of 64? 
4.  Important Notes 
5.  Thinking Out of the Box! 
6.  FAQs on Square Root of 64 
What Is the Square Root of 64?
The square root of 64 is the number whose square gives the original number.
√64 = 8
The answer obtained on squaring 8 is 64. Hence, 64 is a perfect square.
Is the Square Root of 64 Rational or Irrational?
A rational number is either terminating or nonterminating and has a repeating pattern in its decimal part. We saw that √64 = 8. 8 is a whole number and it can be expressed in the p/q form. Hence, √64 is a rational number.
How to Find the Square Root of 64?
There are different methods to find the square root of any number. Click here to know more about it.
64 is a composite number. The factors of 64 are, 1, 2, 4, 8, 16, 32, and 64.
To find the square root of 64, we will do the following.
 We will use the prime factorization method to obtain one number from each pair of the same numbers and we will multiply them. The factorization of 64 is 2 × 2 × 2 × 2 × 2 × 2, which includes 3 pairs of the same number 2. Thus, the square root of 64 is 2 × 2 × 2 = 8 itself.
 Since 64 is a perfect square, we can also express it as 8 × 8 = 64. The number within the square root which is repeated is 8. Hence, the square root of 64 is 8.
The square root of 64 is 8.
Explore square roots using illustrations and interactive examples
Important Notes:
 64 is a perfect square as the answer obtained after finding the square root is a rational number.
 The square root of 64 can be simplified to 8 either by using the prime factorization of 64 or by expressing 64 as a square of 8.
Think Tank:
 Can the square root of 64 be a decimal value?
 Is √64 a real number?
Square Root of 64 Solved Examples

Example 1: A box has an area of 64 square inches. Is this area equal to the area of another square box of length 8 inches?
Solution
The area of the first box is 64 square inches. To find the area of the other square box, we need to find the product of side with itself. The area of the square box of length 8 inches is 8 × 8 = 64 square inches.
Thus, the box with area 64 square inches is equal to the area of the other square box with length 8 inches. 
Example 2: Find the radius of a circle if its area is 64π square inches.
Solution
Area of a circle is πr^{2} square inches. From the given information, we have
πr^{2} = 64π
r^{2} = 64
By taking the square root on both sides, √r^{2}= √64. We know that the square root of r^{2} is r and square root of 64 is 8.
Thus, the radius of the circle is 8 inches.
FAQs on Square Root of 64
What are the two square roots of 64?
The square roots of 64 are 8 and +8.
Is 64 a perfect square?
Yes, 64 is a perfect square.
Does 64 have a square root?
Yes, 64 has a square root.
Can the square root of 64 be simplified?
64 can be broken down as the product of 2 × 2 × 2 × 2 × 2 × 2 or 8 × 8. The square root of 64 gives the result as 8.
Is the square root of 64 rational or irrational?
The square root of 64 is rational.
Is square root of 64 a real number?
Yes, the square root of 64 is a real number.
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