Last updated on May 26th, 2025
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.
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.
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.
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.
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
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.
Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them.
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
By approximating √37, the equation can be simplified and solved step by step.
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
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.
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
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.