197 LearnersLast updated on December 2nd, 2024
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
Square Root of 37 Examples
Problem 1
Solve the equation: 2x+3√37=45
Explanation
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.
Explanation
Problem 3
Solve the equation: x Solve the equation: x²=37+2x
Explanation
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 United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square root of 37 ?
8.How do technology and digital tools in United States support learning Algebra and Square root of 37 ?
9.Does learning Algebra support future career opportunities for students in United States?
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.
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