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Square Root of 37
Did you know 37 is the 12^{th }prime number? Hence, it has only 2 factors, 1 and the number itself (37). In this minilesson let us learn to calculate the square root of 37 using the long division and approximation methods and to express the square root of 37 in the simplest radical form.
 Square Root of 37: √37 = 6.082
 Square of 37: 37^{2} = 1369
What Is the Square Root of 37?
 The square root of 37 is 37 raised to the power ½. 37^{½ }= (number × number) ^{½} = √37
 6.082 × 6.082 = √37 and  6.082 ×  6.082 = √37
 √37 = ± 6.082
 The square root of 37 in its simplest radical form = √37
Is Square Root of 37 Rational or Irrational?
The square root of 37 is an irrational number where the numbers after the decimal point go up to infinity. √37 = 6. 08276253029822 which cannot be expressed as a rational number of the form p/q. Thus square root of 37 is an irrational number.
How to Find the Square Root of 37?
The square root of 37 or any number can be calculated in many ways. To mention a few: Prime factorization method, approximation method and the long division method.
Square Root of 37 by Approximation method
√37 lies between √36 and √49 Clearly, √36 lies closer to 6, as we know 6 × 6 = 36. Use the average method to determine the approximate value of √37.
 The square root of 37 lies between the square root of 36 and the square root of 49. Hence, √36 < √37 < √49 ⇒ 6 < √37 < 7
 Divide 37 by 7. 37 ÷ 7 = 5.28
 Find the average between 5.28 and 7.
 (5.28 + 7)/ 2 = 12.28 /2 = 6.04
 Thus, √37 ≈ 6.04
Square Root of 37 by the Long Division Method
The long division method helps us to find the more accurate value of the square root of any number. Let's see how to find the square root of 37 by the long division method. Here are the desirable steps to be followed.
 Write 37 as 37. 00 00 00.Take 37 as a pair. Find a number × number such that the product is less than or equal to 37.
 We determine that 6 × 6 = 36. subtract this from 37. Get the remainder as 1 and bring down the first pair of zeros. 1 00 is our new divisor.
 Place the decimal point after 6 in the quotient. Multiply the quotient by 2 and have 12x as the new divisor.
 Find a number in the place of x such that 12x × x gives 100 or less than that. We find no such number. So 120 × 0 is 0. Subtract it from 100 and get the remainder as 10. Bring down the next pair of zeros. 1 00 00 is our new divisor.
 Multiply the quotient by 2 and have 120x as the new divisor.
 Find a number in the place of x such that 120x × x gives 10 00 00 or less than that. We find 1208 × 8 is 94 64. Subtract it from 10 00 00 and get the remainder as 3 36.
 Repeat the process until we approximate to 3 decimal places.
 Thus √37 = 6.082 to the nearest thousandths.
Explore Square roots using illustrations and interactive examples
Important Notes
 The square root of 37 is √37 = 37 ^{½ }= ± 6.082.
 The square root of 37 lies between the two perfect squares 36 and 49.
 √37 is irrational.
Challenging Questions
 Find the smallest integer that has to be added to 37 and subtracted from 37 to make it a perfect square. Also find the square root of those perfect squares.
 Find the square root of √37.
Square Root of 37 Solved Examples

Example 1: Evaluate (2 √37 + √37) × 4√37.
Solution:
2 √37 + √37 = (2 + 1) √37 = 3√37
3√37 × 4√37 = 12√37Hence, (2 √37 + √37) × 4√37= 12√37
(2 √37 + √37) × 4√37 = 12√37

Example 2: Evaluate √0.37
Solution:
√0.37= √(37/100)
√(37/100) = √37/√100
As, √37 = 6.082 and √100 = 10
√37/√100 = 6.082 /10 = 0.6082
Thus, √0.37 = 0.6082
FAQs On Square Root of 37
What is the square root of 37?
The square root of 37 is ± 6.082.
How do you write square root of 37 in its simplified form?
√37 is the simplest radical form of the square root of 37.
37 is the square root of which number?
37 is the square root of 1369.
Is square root of 37 a rational number?
Square root of 37 is an irrational number, because the value of √37 is a nonteminating decimal as √37 = 6. 08276253029822.
How to find the square root of 37?
The accurate value of 37 can be evaluated using the long division method.
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