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 x² = 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

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 non-recurring and non-terminating 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

The square root of 450 is a non-repeating and non-terminating 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 non-recurring and non-terminating decimal number. This shows that 450 isn't a perfect square, which also proves that the square root of 450 is an irrational number.

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

• 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

• Square Root of 361
• Square Root of 324
• Square Root of 289
• Square Root of 400
• Square Root of 250
• Square Root of 45
• Square Root of 50
• Square Root of 500

• 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