265 LearnersLast updated on May 26th, 2025
Square root of 37
Square root is simply a number value that when multiplied with itself gives the original number. We apply square roots when we make financial estimations and solve practical problems in geometry.
What is the square root of 37?
The square root is the number that gives the original number when squared.
√37 = 6.08276253 in exponential form, it is written as √37 =371/2.
In this article we will learn more about the square root of 37, how to find it and common mistakes one may make when trying to find the square root.
Finding the square root of 37
To find the square root of a number of students learn many methods. When a number is a perfect square and the process of finding square root is simple.
Square root of 37 using the prime factorization method
Breakdown 37 into prime factors, group them and the result is the square root.
Prime factorization of 37;
37= 37×1
All prime factors cannot be paired and 37 cannot be simplified to a perfect square. Hence, the square root of 37 cannot be expressed in simple radical form.√37 is irrational.
Square root of 37 using the division method
For non-perfect squares, we often use the nearest perfect square value to find the value of a square root. Follow the below steps;
Step 1: Pair 37 with zeros, as it has no decimals in it.
37.00→ (37)(00)
Step 2: pick a number whose square is ≤ 37, 62=36
— 6 is the quotient.
— Subtract the numbers, 37-36=1.
— Bring down the numbers next to the remainder.
Step 3: double quotient and use it as the first digit of the new divisor’s
— Double 6
— Now find the digit x in a way that 2x×x ≤ 100
— x is 9, 29×9 = 261.
Step 4: Now find the final quotient
The result; √37 = 6.0827
Square root of 37 using the approximation method
In the approximation method, we estimate the square root by considering the closest perfect square to 37.
Follow the below steps;
Step 1: Nearest perfect square to 37 → √36=6 and √49 = 7
Step 2: 37 falls between 36 and 49 therefore the square root falls between 6 and 7
Step 3: We try to test numbers like 6.1,6.08 and further. We find that √37 = 6.0827.
Common Mistakes and How to Avoid Them in the Square Root of 37
Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them.
Mistake 1
Rounding the numbers too soon
Rounding 6.0827 to 6.0 too early can result in inaccuracies when applying the square root.
Mistake 2
Getting confused between square root and squaring
The square, 372 is, 1369 and the square root, √37 is 6.0827. Squaring and square rooting are inverse operations and cannot be used interchangeably.
Mistake 3
Assuming incorrectly that 37 is a perfect square
37 is a non-perfect square and does not have a whole-number square root. Find the square roots using the approximation or long division method to make sure precision.
Square Root of 37 Examples
Problem 1
Solve the equation: 2x+3√37=45
Step 1: Substitute the approximate value of √37 ≈ 6.08 into the equation:
2x+3(6.08)=45
Step 2: Simplify:
2x+18.24=45
Step 3: Subtract 18.24 from both sides:
2x=26.76
Step 4: Divide by 2:
x=26.76/2=13.38
Explanation
By approximating √37, the equation can be simplified and solved step by step.
Problem 2
The diagonal of a rectangle is 37 cm. If the length of the rectangle is 32 cm, find the width of the rectangle.
Use the Pythagorean theorem:
Diagonal2=Length2+Width2
Substitute the known values:
372=322+w2
Solve for the width (w):
w2=1369=1024+w2
w=√345≈18.57 cm
Explanation
Using the Pythagorean theorem, we find the width by subtracting the square of the length from the square of the diagonal and then taking the square root of the result.
Problem 3
Solve the equation: x Solve the equation: x²=37+2x
Step 1: Rearrange the equation:
x2−2x−37=0
Step 2: Use the quadratic formula x=−b±√b2−4ac/2a, where a=1, b=−2, c=−37:
x= −(−2)±√(−2)2−4(1)(−37)/2(1)
x=2±√4+148/2
x=2±√152/2
Since 152≈12.33:
x=2±12.33/2
Step 3: Solve for x:
x=2+12.33/2≈7.17or x=2−12.33/2≈−5.17
Explanation
By applying the quadratic formula and approximating the square root of 152, we find the two possible solutions for x: 7.17 or -5.17.
FAQs on the Square root of 37
1.Are 36 perfect squares?
2.What is √34?
3.What is √47?
4.Is 1000 a perfect square?
5.What is the square root of 0?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square root of 37 ?
8.How do technology and digital tools in Thailand support learning Algebra and Square root of 37 ?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important glossaries for the square root of 37
- Prime numbers — Any number that has only two factors, 1 and the number itself, is called a prime number. Prime numbers up to 10 are — 2,3,5,7.
- Integer — A number between zero and infinite, that can be positive or negative, fraction or decimal.
- Perfect square number — a number whose square root has no decimal places in them. For example, the square root of 37.
- Non-perfect square numbers — A number whose square has a fraction or decimal in its result. For example, square root of 37.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
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