The square source of 300 is expressed as √300 in the radical type and together (300)½ or (300)0.5 in the exponent form. The square root of 300 rounded up to 9 decimal places is 17.320508076. That is the positive solution of the equation x2 = 300. We deserve to express the square root of 300 in its lowest radical kind as 10 √3.

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What Is the Square source of 300?

The square root of a number n is written as √n. This number when squared or multiply by itself outcomes in the initial number n. The square source of 300 can be written in many ways:


Radical form: √300 = 10√3Decimal form: 17.320Exponent form: (300)1/2

Is Square source of 300 rational or Irrational?


How to find the Square source of 300?

There space 2 crucial methods to find the square root of 300.


Long department MethodPrime Factorization

One can discover out other methods by clicking here

Long department Method

The square source of 300 by long department method is composed of the adhering to steps:

Step 1: Starting native the right, we will pair increase the digits 300 by putting a bar above 00 and also 3 separately. We will also pair the 0s in the decimal from left come right.Step 4:  Find a number X such that 2X × X outcomes in a number less than or same to 200. The number 7 fits here, so location it next to 2 in the divisor as well as next to 1 in the quotient. Step 5: uncover the remainder and also now drag down the pair that 0s indigenous the decimal part of the number. Dual the quotient to acquire the new divisor. The brand-new divisor is 34. Step 6: Repeat this procedure to obtain the decimal areas you want.

See more: What Is 16 Divided By 6 Divided By 3/4? What Is 16 Divided By 3/4

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Therefore, the square source of 300 = 17.320

Prime Factorization

Next, this have the right to be decreased further to300 = 22 × 3 × 52It is now easy to uncover the root from here:√300 = √(22 × 3 × 52)√300 = 10√3 = 17.320

Therefore, the square root of 300 ≅ 17.320

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Important Notes


There exist a hopeful and negative root of 300; 17.320 and also -17.320There will certainly be n/2 number in the square root of an also number v n digits.There will be (n+2)/2 number in the square source of an odd number with n digits.