Square Root of 450
The square root of 450 is expressed as √450 in the radical form and as (450)^{½} or (450)^{0.5} in the exponent form. The square root of 450 rounded up to 10 decimal places is 21.2132034356. It is the positive solution of the equation x^{2} = 450. We can express the square root of 450 in its lowest radical form as 15 √2.
 Square Root of 450: 21.213203435596427
 Square Root of 450 in exponential form: (450)^{½} or (450)^{0.5}
 Square Root of 450 in radical form: √450 or 15 √2
1.  What is the Square Root of 450? 
2.  Is Square Root of 450 Rational or Irrational? 
3.  How to Find the Square Root of 450? 
4.  FAQs on Square Root of 450 
What Is the Square Root of 450?
It is not possible to break 450 into two equal factors which, on multiplying, give 450. It can be approximately written as a square of 21.21, which is a nonrecurring and nonterminating decimal number. This shows that it is not a perfect square, which also proves that the square root of 450 is an irrational number. Do you think the square root of 450 and the square root of 45 have anything in common? Yes, there is. Both are not perfect squares. So, √450 is an irrational number. If a number is a perfect square, it is easy to evaluate the square root using the inverse operation of the squaring operation. 450 is not a perfect square. √450 can be evaluated using the long division method. The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 450 can be written as:
 Radical form: √450
 Decimal form: 21.21
 Exponent form: (450)^{½}
Is Square Root of 450 Rational or Irrational?
The square root of 450 is a nonrepeating and nonterminating number. So, it cannot be expressed in the form of p/q where q ≠ 0. Hence, the square root of 450 is an irrational number. 450 cannot be broken into two equal factors which on multiplying give 450. It can be approximately written as a square of 21.21, which is a nonrecurring and nonterminating decimal number. This shows that 450 isn't a perfect square, which also proves that the square root of 450 is an irrational number.
How to Find the Square Root of 450?
There are 2 ways to find the square root of 450:
 Long Division Method
 Prime Factorization
Long Division Method
The square root of 450 by long division method consists of the following steps:
 Pair the digits from the right side in pairs of two by putting a bar on top of them. In the case of 450, we will have two pairs, 50 and 4 (pairing from right).
 Now we have to find a number(y) whose square is ≤ 4. The value of z will be 2 as 2 × 2 = 4 = 4.
 We get the quotient (2) and the remainder (0). Now, add the divisor z with itself and get the new divisor 2z (4).
 Drag the pair of zero (new dividend becomes 50) and find a number (a) such that 4a × a ≤ 50. The value of a comes out to be 1.
 Now, add a decimal in the dividend part (450) and quotient part (21.2) simultaneously. Also, add 3 pairs of zero in the dividend part after the decimal and repeat the above step for the other three pairs of zero as well.
So, we get the value of the square root of √450 = 21.21 by the long division method.
Therefore, the square root of 450 = 21.213
The square root of 450 by prime factorization:
Prime factorization of 450 = 2 × 3 × 3 × 5 × 5
Simplified form of √450 is = 15√2
Square root of 2 is 1.4142.
√450 = 15 × 1.4142 = 21.213
Therefore, the square root of √450 = 21.213
Important Notes:
 450 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Square root of 450 is simplified in decimal form as √450 = 21.213
 Square root of 450 cannot be expressed as a fraction if the form p/q which tells us that the square root of 450 is an irrational number.
Explore square roots using illustrations and interactive examples
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Challenging Questions
 What is the negative root of 4500?
 Find the square root of 450 up to 5 decimal places?
 What is the square root of:
a) 450000
b) √4500
Solved Examples

Example 1: The area of square shaped plot is 202,500 square units. Calculate the measurement of one side of a land.
Solution:
The area of land = 202,500 sq. units
To find the side of a squareshaped plot, let us take the square root of 202,500 by prime factorization method.
Prime factorization of 202,500 = 450 × 450
√202,500 = 450
Therefore, the square root of √202,500 = 450
Therefore, side of square plot is 450 units. 
Example 2: What number Tiya should be multiplying with 450 to obtain a perfect square number 484?
Solution:
To find the number, let us assume number = a
On multiplying 450 times a = 484
a = 484 ÷ 450
a = 1.0755
450 × 1.0755 = 483.975 ≅ 484
The number is 1.0755. 
Example 3: What number should Risa add to 450 to obtain a perfect square number. If the square root of the obtained number is 22, find the number. Find if the obtained number is also a perfect square.
Solution:
To find the number let us assume number = a
On adding 'a' we get,
450 + a = (22)²
a = 484  450
a = 34
450 + 34 = 484.
484 is a perfect square (√484 = 22).
34 is not a perfect square number √34 = 5.8309
The number is 34, and it is not a perfect square.
FAQs on the Square Root of 450
What is the Value of the Square Root of 450?
The square root of 450 is 21.2132.
Why is the Square Root of 450 an Irrational Number?
Upon prime factorizing 450 i.e. 2^{1} × 3^{2} × 5^{2}, 2 is in odd power. Therefore, the square root of 450 is irrational.
What is the Square Root of 450?
The square root of 450 is an imaginary number. It can be written as √450 = √1 × √450 = i √450 = 21.213i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 450 in Simplest Radical Form?
We need to express 450 as the product of its prime factors i.e. 450 = 2 × 3 × 3 × 5 × 5. Therefore, √450 = √2 × 3 × 3 × 5 × 5 = 15 √2. Thus, the square root of 450 in the lowest radical form is 15 √2.
What is the Square of the Square Root of 450?
The square of the square root of 450 is the number 450 itself i.e. (√450)^{2} = (450)^{2/2} = 450.
Evaluate 20 plus 14 square root 450
The given expression is 20 + 14 √450. We know that the square root of 450 is 21.213. Therefore, 20 + 14 √450 = 20 + 14 × 21.213 = 20 + 296.985 = 316.985
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