Square Root of 1296

The square root of 1296 is also called root 1296 in short form. The square root of a number can be a rational/irrational number, positive/negative number, real/imaginary number. 1296 is a special number with its square root being a perfect square. Now we will see some cool facts about the square root of 1296 and few interesting problems as well.

• Square root of 1296: 36
• Square of 1296: 16,79,616

• The square root of 1296 can be represented as √1296 and (1296)^1/2
• The square of 1296 will be a number(n) such that n × n = 1296
  36 × 36 = 1296 also -36 × -36 = 1296
  Therefore, +36 and -36 are the square roots of 1296.

The square roots of 1296 are +36 and -36. Both numbers are integers and all integers are rational numbers. Therefore, the square root of 1296 is a rational number.

Now we will find the square root of 1296 using the prime factorization and long division methods.

Square Root of 1296 by Prime Factorization Method

• Prime factorization of 1296: 2⁴ × 3⁴
• Prime factors of 1296 in pairs: (2 × 2) × (2 × 2) × (3 × 3) × (3 × 3)
• Square root of 1296: √((2 × 2)² × (3 × 3)²) = (2)² × (3)² = ±36
• Therefore, √1296 = ±36

Square Root of 1296 by Long Division Method

We will now find the square root of 1296 using the long division method:

• Start grouping the digits from the unit’s place in pairs of two by placing a bar on top of them. We have two pairs in this case, 12 and 96.
• Find a number(a) such that a × a ≤ 12. So, a will be 3 as 3 × 3 = 9 ≤ 12.
• We get the remainder and the quotient as 3. Also, add the divisor a with itself (3 + 3). We get the new divisor as 6.
• Bring down the next pair of numbers to form the new dividend. So, the new dividend is 396.
• Find a number(n) such that 6n × n ≤ 396. We get n = 6 as 66 × 6 = 396.

So, we get the square root of √1296 = 36 by the long division method.

Explore square roots using illustrations and interactive examples. 

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• The number 1296 is a perfect square.
• The square root of 1296 is a rational number.
• The square root of -1296 is an imaginary number.

What is the square root of -1296?

The square root of negative numbers is imaginary because squares of both positive and negative numbers result in positive numbers.
The square root of -1296 is represented as ±36i. (where i = √-1)

What is the square of 1296?

Square of the number 1296 is (1296)² = 16,79,616

What is the square root of 1296 in prime factorization form?

The square root of 1296 is √1296 = 36.
Now, the prime factorization of 36 = 2 × 2 × 3 × 3

Can we find the square root of 1296 using the approximation method?

No, we can’t find the square root of 1296 using the approximation method because the number 1296 is a perfect square and this method cannot be used in the case if the given number is a perfect square.

How is the square root of 1296 expressed in exponential and radical form?

• The square root of 1296 is written as (1296)^1/2 in the exponential form.
• The square root of 1296 is written as √1296 in the radical form.