what is the square root of 37

Video Square root of 37 Square root of 37 Did you know 37 is the 12th prime number? Therefore, it has only 2 factors, 1 and the number itself (37). In this mini-lesson, let’s learn how to calculate the square root of 37 using long division and approximation methods and represent the square root of 37 in its simplest form.

  • Square root of 37: 37 = 6.082
  • Square 37: 372 = 1369

1. What is the square root of 37? 2. Is the square root of 37 Reasonable or Unreasonable? 3. How to find the square root of 37? 4. Important Notes about Square Root of 37 5. Challenging Questions 6. Frequently Asked Questions about Square Root of 37

  • The square root of 37 is raised to a power of ½. 37½ = (number × number) = 37
  • 6.082 × 6.082 = 37 and – 6.082 × – 6.082 = 37
  • 37 = ± 6.082
  • Square root of 37 in its simplest form = 37

The square root of 37 is an irrational number where the numbers after the decimal point go up to infinity. √37 = 6. 0334390000 2 cannot be expressed as a rational number of the form p / q. So the square root of 37 is an irrational number Reading: square root of 37 Read more: What does soy milk taste like The square root of 37 or any number can be calculated in many ways. Some of them can be mentioned: prime factorization method, approximation method and long division method.

Square root of 37 by approximation

√37 lies between √36 and √49 Obviously, √36 lies closer to 6, as we know 6 × 6 = 36. Use the averaging method to determine the approximate value of √37.

  • The square root of 37 is between the square root of 36 and the square root of 49. Thus, √36 < √37 < √49 ⇒ 6 < √37 < 7
  • Divide 37 by 7. 37 7 = 5.28
  • Find the mean between 5.28 and 7.
  • (5.28 + 7) / 2 = 12.28 / 2 = 6.04
  • Therefore, 37 6.04
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Square root of 37 by length division

Read more: Dynamic NAT The long division method helps us to find more exact value of square root of any number. Let’s see how to find the square root of 37 using the long division method. Below are the desired steps to be followed.

  • Write 37 as 37. 00 00 00. Take 37 as a pair. Find a number × such that the product is less than or equal to 37.
  • We determine that 6 × 6 = 36. subtract 37 from this. Take the remainder 1 and lower 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 get 12x as the new divisor.
  • Find a number in the place of x such that 12x × x returns less than 100. We found no such number. So 120 × 0 is 0. Take that minus 100 and get a remainder of 10. Take the next pair of zeros down. 1 00 00 is our new divisor.
  • Multiply the quotient by 2 and get 120x as the new divisor.
  • Find a number in the place of x such that 120x × x is less than or equal to 10 00 00. We see that 1208 × 8 is 94 64. Subtract 10 00 00 from 10 00 00 and get a remainder of 3 36.
  • Repeat the process until we approximate 3 decimal places.
  • So √37 = 6.082 to the nearest thousandth.

Explore Square Roots using interactive illustrations and examplesRead more: What are character studs in lego games

  • Square root of 36
  • Square root of 54
  • Square root of 16
  • Square root of 26
  • Square root of 60
  • Find the smallest integer that must add 37 and subtract 37 for it to be a perfect square. Also find the square root of those perfect squares.
  • Find the square root of √37.
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