Square Root of 52

The square root of 52 is expressed as √52 in the radical form and as (52)^½ or (52)^0.5 in the exponent form. The square root of 52 rounded up to 9 decimal places is 7.211102551. It is the positive solution of the equation x² = 52. We can express the square root of 52 in its lowest radical form as 2 √13.

• Square Root of 52: 7.211102550927978
• Square Root of 52 in exponential form: (52)^½ or (52)^0.5
• Square Root of 52 in radical form: √52 or 2 √13

• The square root of a number is the number whose product with itself gives the initial number.
• Square root of 52 is √52 = 7.2111
• Square root of 52 can be represented as √52 and (52)^1/2
• The square root of 52 is a non-repeating and non-terminating number.
  Thus, 52 is not a perfect square.

A number is called rational if it can be represented in the form of p/q where q ≠ 0.
The square root of 52 is a number that cannot be represented in this form.
Therefore, the square root of 52 is an irrational number.

We will now calculate the square root of 52 using two different methods.

Square Root of 52 Using Approximation Method

Step1. Find two perfect squares between which 52 lies. The two perfect squares are 49 (7²) and 64 (8²) between which 52 lies. So, we can say that the square root of 52 will be greater than 7 but less than 8 (7 < √52 < 8).
Therefore, the whole number part of the square root will be 7.

Step2. Now for estimating the decimal part, we will use the formula:
(Given number - Lower perfect square) / (Bigger perfect square - Lower perfect square)
Therefore, the decimal part will be = (52-49) / (64-49) = 3/15 = 0.2
So, the approximate square root of 52 will be 7.2

Square Root of 52 by Long Division

With the help of the steps given below, we will now find the square root of 52 by the long division method.

• Start grouping the digits from the right side in pairs of two by putting a bar on top of them. As there are only two digits in 52, we have only one pair.
• Find a number whose product with itself results in a number less than or equal to 52. The number will be 7 as 7 × 7 = 49.
• We get the quotient 7 and the remainder as 3 (52 - 49) and by adding 7 with itself we get the new divisor as 14. As no more numbers are left in the dividend, add a decimal after the dividend and quotient.
• Now add three pairs of zero after the decimal in the dividend part and bring down the first pair of zeros. 
• Look for a number(n) such that 14n × n results in a number less than equal to 300. Here n will be 2 as 142 × 2 = 284 (less than 300)
• Bring down the next pair of zeros down and repeat the above step till the last pair of zeros.

So, we get a square root of √52 = 7.211 by the long division method.

Explore square roots using illustrations and interactive examples.

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• The number 52 is not a perfect square.
• The square root of 52 is an irrational number.
• The square root of -52 is an imaginary number.