what is the square root of 90

The square root of 9090 is not a perfect square, however, it is a semi-perfect number which means it is the sum of all or some of its divisors. The square root of 90 increases 90 to a half power. In this lesson, we will calculate the square root of 90 using long division and approximation and solve some interesting problems.

  • Square root of 90: 90 = 9.486
  • Square 90: 902 = 8100

1. What is the square root of 90? 2. Is the square root of 90 Reasonable or Unreasonable? 3. How to Find the Square Root of 90? 4. FAQ about Square Root of 90

  • The square root of a number is a number that, when multiplied by itself, gives the original number the product.
  • n × n = 90. This shows that the square of a number is 90.
  • n = 90 or n = 90½
  • 90 = 3 × 3 × 10 = 32 × 10
  • So 90 = (32 × 10)
  • Squared on both sides, 90½ = 3√10
  • Therefore, the simple form of 90 = 3√10
  • The value of 90 is evaluated as 9,486832980505138
  • A rational number is defined as a number that can be expressed as the quotient or division of two integers, i.e. p/q, where q is not zero.
  • 90 = 9,486832980505138
  • Therefore √90 is not reasonable.

The square root of 90 can be calculated using different methods such as prime factorization or long division method or average method. By the prime factorization method, we see that the simplest root form √90 is 3√10. Read: What is the square root of 90

Square root of 90 by approximation

  • Find the 2 closest perfect squares to 90. They are 81 and 100. 81 < 90 < 100
  • 81 <√90 <√100
  • 9 <√90 <10
  • Divide 90 by 9 or 10. divide by 9. 90 9 = 10
  • Find the mean of this quotient and 9 (10 +9) 2
  • 19 2 = 9.5
  • So 90 9.5
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Square root of 90 by length division method

  • Write 90 in pairs after the decimal point 90.00 00 00.
  • Find a number x of that number for 90 or less. We find 9 × 9 = 81. subtract 81 from 90 and get 9 as the remainder.
  • Bring down the next pair of zeros. 900 becomes the new dividend.
  • Multiply the quotient obtained in the previous step by 2. It is 18. Now 180 is written in place of the new divisor.
  • Find a number that is added to the units row by 180 such that the sum when multiplied by the number is 900 or less. We determine that 180 + 4 = 184 and 184 × 4 = 736.
  • Subtract this number from 900. It is 164 and get the new divisor by crossing out the next pair of zeros. 16400 is our new dividend.
  • Repeat the process until we estimate the value to 3 decimal places.
  • Therefore, √90 = 9,486.

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  • Square root of 85
  • Square root of 900
  • Square root of 98
  • Square root of 89
  • Square root of 65
  • Know that 90 lies between the perfect squares 81 and 100 and therefore the square root of 90 lies between 9 and 10.
  • Use the mean method to approximate the square root of 90.
  • The square root of 90 is expressed as 3√10 in root form and 90½ in exponential form.
  • 90 = ±9.486832980505138

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