what is the square root of 75

The square root of 7575 is an odd composite number. The square root of 75 is 75 raised to a half power. In this mini-lesson, let’s learn about the square root of 75, find out if the square root of 75 is rational or irrational, and see how to find the square root of 75 using the long division method.

  • Square root of 75: 75 = 8.66
  • Square 75: 752 = 5625

1. What is the square root of 75? 2. Square root of 75 Reasonable or Unreasonable? 3. How to Find the Square Root of 75? 4. FAQ about Square Root of 75

  • The square root of 75 can be written as √75.
  • That means there exists a number a such that a × a = 75. It can also be written as: a2 = 75.
  • a = √75. a is the square root of 75 and a = 8.66
  • The square root of any number has two values; one is positive and the other is negative. So 75 = +8.66 or – 8.66
  • In exponentiation, we denote 75 as (75)
  • We know that 75 = 5 × 5 × 3. In the simplest radical form √75 = 5√3

The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8,660.√75 cannot be written as p/q, so it is irrational topqa.infotional with never ending digits. The square root of 75 or any number can be calculated in several ways. Two of them are the average method and the long division method.

Square root of 75 by the mean method

  • Take two perfect squares that are both less than 75 and greater than 75. 64 < 75 < 81
  • 8 <√ 75 < 9
  • Using the average method, divide 75 by 8 or 9.
  • We divide by 9. 75 9 = 8.33
  • Find the mean of 8.33 and 9
  • (8.33 + 9) / 2 = 17.33 2 = 8.66
  • 75 8.66
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Square root of 75 by length division method

The long division method helps us to find the more exact value of the square root of any number. Read more: What is a frat party Let’s see how to find the square root of 75 using the long division method.

  • Step 1: Express 75 as 75.000000. We take numbers in pairs from the right. Take 75 as a dividend.
  • Step 2: Now find a quotient that is the same as the divisor. Multiply the quotient by the divisor and subtract the result by 75.
  • Step 3: Now double the quotient obtained in step 2. This is 2 × 8 = 16. 160 becomes the new divisor.
  • Step 4: Apply the decimal after the quotient ‘8’ and reduce the two zeros. We have 1100 as dividends now.
  • Step 5: We need to choose a number that when we add 160 and multiply by the same number, we get a number less than 1100. 160 + 6 = 166 and 166 × 6 = 996. Take 1100 minus 996 to get 104.
  • Step 6: Reduce two zeros again and put it after 104, so that it becomes 10400, which is the new dividend. Now multiply the number in the quotient by 2. This is 86. We get 172. Yes it’s 1720. Now find a number in the units of 1720 multiplying by itself gives 10400 or less. We see that 1726 × 6 = = 10356. Find the remainder.
  • Step 6: Repeat the process until we get a remainder of zero. The square root of 75 has two degrees obtained by the long division method. So 75 = 8.66
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Explore square roots using interactive illustrations and examples. Read more: Difference between Hard Iron and Soft Iron | Top Q&A

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  • The square root of any number can be assumed to be the middle of the square root of the two nearest perfect squares of that number. For example, the square root of 75 is between the square root of 64 and 81. √64 < √56 < √81, that is, 8 < √75 < 9. Then use the average method to find the approximate value.
  • We just multiply 75 by 3 to make it a perfect square. This is because, 75 = 5 × 5 × 3. 3 does not have a pair. So 75 × 3 = 225 and √225 is 15.
  • The square root of 75 is 8,660 which is approximately 3 decimal places.
  • The simple form of 75 in its root form is 5√3
  • √75 is an irrational number.

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