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Square Root of 1100

The square root of 1100 is expressed as √1100 in the radical form and as (1100)½ or (1100)0.5 in the exponent form. The square root of 1100 rounded up to 8 decimal places is 33.16624790. It is the positive solution of the equation x2 = 1100. We can express the square root of 1100 in its lowest radical form as 10 √11.

  • Square Root of 1100: 33.166247903554
  • Square Root of 1100 in exponential form: (1100)½ or (1100)0.5
  • Square Root of 1100 in radical form: √1100 or 10 √11

Square Root of 1100

1. What is the Square Root of 1100?
2. How to find the Square Root of 1100?
3. Is the Square Root of 1100 Irrational?
4. FAQs

What is the Square Root of 1100?

The square root of 1100, (or root 1100), is the number which when multiplied by itself gives the product as 1100. Therefore, the square root of 1100 = √1100 = 10 √11 = 33.166247903554.

☛ Check: Square Root Calculator

How to Find Square Root of 1100?

Square Root of 1100 by Long Division Method

Value of √1100 by Long Division Method

Explanation:

  • Forming pairs: 11 and 00
  • Find a number Y (3) such that whose square is <= 11. Now divide 11 by 3 with quotient as 3.
  • Bring down the next pair 00, to the right of the remainder 2. The new dividend is now 200.
  • Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 3) such that 6Z × Z <= 200. After finding Z, together 6 and Z (3) form a new divisor 63 for the new dividend 200.
  • Divide 200 by 63 with the quotient as 3, giving the remainder = 200 - 63 × 3 = 200 - 189 = 11.
  • Now, let's find the decimal places after the quotient 33.
  • Bring down 00 to the right of this remainder 11. The new dividend is now 1100.
  • Add the last digit of quotient to divisor i.e. 3 + 63 = 66. To the right of 66, find a digit Z (which is 1) such that 66Z × Z <= 1100. Together they form a new divisor (661) for the new dividend (1100).
  • Divide 1100 by 661 with the quotient as 1, giving the remainder = 1100 - 661 × 1 = 1100 - 661 = 439.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1100.

Therefore, the square root of 1100 by long division method is 33.1 approx.

Is Square Root of 1100 Irrational?

The actual value of √1100 is undetermined. The value of √1100 up to 25 decimal places is 33.16624790355399849114933. Hence, the square root of 1100 is an irrational number.

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Square Root of 1100 Solved Examples

  1. Example 1: Solve the equation x2 − 1100 = 0

    Solution:

    x2 - 1100 = 0 i.e. x2 = 1100
    x = ±√1100
    Since the value of the square root of 1100 is 33.166,
    ⇒ x = +√1100 or -√1100 = 33.166 or -33.166.

  2. Example 2: If the area of an equilateral triangle is 1100√3 in2. Find the length of one of the sides of the triangle.

    Solution:

    Let 'a' be the length of one of the sides of the equilateral triangle.
    ⇒ Area of the equilateral triangle = (√3/4)a2 = 1100√3 in2
    ⇒ a = ±√4400 in
    Since length can't be negative,
    ⇒ a = √4400 = 2 √1100
    We know that the square root of 1100 is 33.166.
    ⇒ a = 66.332 in

  3. Example 3: If the area of a circle is 1100π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 1100π in2
    ⇒ r = ±√1100 in
    Since radius can't be negative,
    ⇒ r = √1100
    The square root of 1100 is 33.166.
    ⇒ r = 33.166 in

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FAQs on the Square Root of 1100

What is the Value of the Square Root of 1100?

The square root of 1100 is 33.16624.

Why is the Square Root of 1100 an Irrational Number?

Upon prime factorizing 1100 i.e. 22 × 52 × 111, 11 is in odd power. Therefore, the square root of 1100 is irrational.

Evaluate 6 plus 15 square root 1100

The given expression is 6 + 15 √1100. We know that the square root of 1100 is 33.166. Therefore, 6 + 15 √1100 = 6 + 15 × 33.166 = 6 + 497.494 = 503.494

Is the number 1100 a Perfect Square?

The prime factorization of 1100 = 22 × 52 × 111. Here, the prime factor 11 is not in the pair. Therefore, 1100 is not a perfect square.

What is the Square Root of -1100?

The square root of -1100 is an imaginary number. It can be written as √-1100 = √-1 × √1100 = i √1100 = 33.166i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 1100 in Simplest Radical Form?

We need to express 1100 as the product of its prime factors i.e. 1100 = 2 × 2 × 5 × 5 × 11. Therefore, √1100 = √2 × 2 × 5 × 5 × 11 = 10 √11. Thus, the square root of 1100 in the lowest radical form is 10 √11.

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