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Square Root of 333

The square root of 333 is expressed as √333 in the radical form and as (333)^½ or (333)^0.5 in the exponent form. The square root of 333 rounded up to 8 decimal places is 18.24828759. It is the positive solution of the equation x² = 333. We can express the square root of 333 in its lowest radical form as 3 √37.

Square Root of 333: 18.24828759089466
Square Root of 333 in exponential form: (333)^½ or (333)^0.5
Square Root of 333 in radical form: √333 or 3 √37

Square Root of 333

1.	What is the Square Root of 333?
2.	How to find the Square Root of 333?
3.	Is the Square Root of 333 Irrational?
4.	FAQs

What is the Square Root of 333?

The square root of 333, (or root 333), is the number which when multiplied by itself gives the product as 333. Therefore, the square root of 333 = √333 = 3 √37 = 18.24828759089466.

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How to Find Square Root of 333?

Square Root of 333 by Long Division Method

Value of √333 by Long Division Method

Explanation:

Forming pairs: 03 and 33
Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
Bring down the next pair 33, to the right of the remainder 2. The new dividend is now 233.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 8) such that 2Z × Z <= 233. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 233.
Divide 233 by 28 with the quotient as 8, giving the remainder = 233 - 28 × 8 = 233 - 224 = 9.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 2) such that 36Z × Z <= 900. Together they form a new divisor (362) for the new dividend (900).
Divide 900 by 362 with the quotient as 2, giving the remainder = 900 - 362 × 2 = 900 - 724 = 176.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 333.

Therefore, the square root of 333 by long division method is 18.2 approx.

Is Square Root of 333 Irrational?

The actual value of √333 is undetermined. The value of √333 up to 25 decimal places is 18.24828759089465906699905. Hence, the square root of 333 is an irrational number.

☛ Also Check:

Square Root of 105 - √105 = 10.24695
Square Root of 48 - √48 = 6.92820
Square Root of 1024 - √1024 = 32
Square Root of 288 - √288 = 16.97056
Square Root of 16 - √16 = 4
Square Root of 49 - √49 = 7
Square Root of 136 - √136 = 11.66190

Square Root of 333 Solved Examples

Example 1: Solve the equation x² − 333 = 0

Solution:

x² - 333 = 0 i.e. x² = 333
x = ±√333
Since the value of the square root of 333 is 18.248,
⇒ x = +√333 or -√333 = 18.248 or -18.248.
Example 2: If the surface area of a sphere is 1332π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1332π in²
⇒ r = ±√333 in
Since radius can't be negative,
⇒ r = √333
The square root of 333 is 18.248.
⇒ r = 18.248 in
Example 3: If the area of a circle is 333π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 333π in²
⇒ r = ±√333 in
Since radius can't be negative,
⇒ r = √333
The square root of 333 is 18.248.
⇒ r = 18.248 in

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FAQs on the Square Root of 333

What is the Value of the Square Root of 333?

The square root of 333 is 18.24828.

Why is the Square Root of 333 an Irrational Number?

Upon prime factorizing 333 i.e. 3² × 37¹, 37 is in odd power. Therefore, the square root of 333 is irrational.

What is the Square Root of 333 in Simplest Radical Form?

We need to express 333 as the product of its prime factors i.e. 333 = 3 × 3 × 37. Therefore, √333 = √3 × 3 × 37 = 3 √37. Thus, the square root of 333 in the lowest radical form is 3 √37.

What is the Square Root of -333?

The square root of -333 is an imaginary number. It can be written as √-333 = √-1 × √333 = i √333 = 18.248i
where i = √-1 and it is called the imaginary unit.

Is the number 333 a Perfect Square?

The prime factorization of 333 = 3² × 37¹. Here, the prime factor 37 is not in the pair. Therefore, 333 is not a perfect square.

If the Square Root of 333 is 18.248. Find the Value of the Square Root of 3.33.

Let us represent √3.33 in p/q form i.e. √(333/100) = 3.33/10 = 1.825. Hence, the value of √3.33 = 1.825

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