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Square Root of 900

The square root of 900 is expressed as √900 in the radical form and as (900)½ or (900)0.5 in the exponent form. The square root of 900 is 30. It is the positive solution of the equation x2 = 900. The number 900 is a perfect square.

  • Square Root of 900: 30
  • Square Root of 900 in exponential form: (900)½ or (900)0.5
  • Square Root of 900 in radical form: √900
1. What Is the Square Root of 900?
2. Is Square Root of 900 Rational or Irrational?
3. Important Notes on Square Root of 900
4. How to Find the Square Root of 900?
5. Thinking Out of the Box!
6. FAQs on Square Root of 900

What Is the Square Root of 900?

The square root of a number is a number whose square gives the original number. For example, to find the square root of 900 (which is denoted by √900), we have to think of a number that multiplies by itself to give 900. In short, a square root is a number which when squared gives the original number.

Square root of 900

You can remember it this way: When the square moves from one side to the other side of the equation, it becomes the square root. 302 = 900 ⇒ √900 = 30. Thus, the square root of 900 is 30.

Is Square Root of 900 Rational or Irrational?

A rational number can be expressed as a fraction of integers. We already found that √900 = 30 = 30/1, so we could express √900 as a fraction of integers and hence it is a rational number.

Important Notes

  1. If we do not have pairs of the same numbers as above, then the prime factorization cannot be used to find the exact square root. Instead, we have to use the long division method.
  2. The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.

How to Find Square Root of 900?

We can find the square root of 900 using various methods.

  1. Repeated Subtraction
  2. Prime Factorization
  3. Estimation and Approximation
  4. Long Division

Should you wish to learn more about each of these methods, you may learn it here. Since we could find that 900 is a perfect square, we can find its square root using the prime factorization easily.

Square Root of 900 Using Prime Factorization

The prime factorization of 900 can be found as 2 × 2 × 3 × 3 × 5 × 5. To find the square root of 900, we take one number from each pair of the same numbers and we multiply them.
Hence, √900 =√(2 × 2 × 5 × 5 × 3 × 3) = 2 × 5 × 3 = 30

Square Root of 900 by Long Division

The square root of 900 can be found using the long division as follows:
Think of a number which when multiplied by itself gives a number that is less than or equal to 900 or a number that is very close to 900. 

Square root of 900 by long division

Since the remainder is 0, we do not need to proceed with long division further and we consider the quotient (which is 30) as the result. 

Think Tank

  • Can the value of √900 be -30 as well? Hint: Think what is (−30)2.
  • Is √−900 a real number? Think about whether there is any real number whose square is negative.

Explore Square roots using illustrations and interactive examples

 

Square Root of 900 Solved Examples

  1. Example 1 John is instructed to find the square root of 900 using the laws of exponents. Can you help him with this?

    Solution

    The square root can be always replaced with the exponent 1/2.
    √900= 9001/2 = (302)1/2    [∵ 302 = 900] = 30
    Thus, ∴ √900=30

  2.  

    Example 2  Daniel is trying to figure out whether 900 and 2500 are perfect squares. What method can he use to find the square roots of 2500 and 900 quickly?

    Solution

    Daniel can figure out the square root of 2500 and the square root of 900 by various methods. By using the division method, he will get:
    2500 ÷ 50 = 50
    Therefore, 50 × 50 = 2500, and hence, 2500 is a perfect square with square root 50
    Also,
    900 ÷ 30=30
    Therefore, 30 × 30 = 900, and hence, 900 is a perfect square with square root 30

  3. Example 3 If the area of a circle is 900π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 900π in2
    ⇒ r = ±√900 in
    Since radius can't be negative,
    ⇒ r = √900
    The square root of 900 is 30.
    ⇒ r = 30 in

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FAQs on the Square Root of 900

What is the Value of the Square Root of 900?

The square root of 900 is 30.

Why is the Square Root of 900 a Rational Number?

Upon prime factorizing 900 i.e. 22 × 32 × 52, we find that all the prime factors are in even power. This implies that the square root of 900 is a positive integer. Therefore, the square root of 900 is rational.

If the Square Root of 900 is 30. Find the Value of the Square Root of 9.

Let us represent √9 in p/q form i.e. √(900/100) = 30/10 = 3.0. Hence, the value of √9 = 3.0

What is the Square Root of -900?

The square root of -900 is an imaginary number. It can be written as √-900 = √-1 × √900 = i √900 = 30i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 900?

The square of the square root of 900 is the number 900 itself i.e. (√900)2 = (900)2/2 = 900.

Evaluate 13 plus 10 square root 900

The given expression is 13 + 10 √900. We know that the square root of 900 is 30. Therefore, 13 + 10 √900 = 13 + 10 × 30 = 13 + 300 = 313

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