The square source of 300 is expressed as √300 in the radical form and as (300)½ or (300)0.5 in the exponent form. The square source of 300 rounded as much as 9 decimal areas is 17.320508076. It is the hopeful solution the the equation x2 = 300. We deserve to express the square root of 300 in its shortest radical form as 10 √3.

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What Is the Square source of 300?

The square source of a number n is composed as √n. This number once squared or multiply by itself outcomes in the original number n. The square source of 300 deserve to be created in multiple 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 room 2 necessary methods to discover the square root of 300.


Long department MethodPrime Factorization

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Long department Method

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

Step 1: Starting indigenous the right, we will pair up the digits 300 by placing a bar over 00 and also 3 separately. We will likewise pair the 0s in the decimal from left to right.Step 4:  Find a number X such the 2X × X outcomes in a number much less than or equal to 200. The number 7 fits here, so location it next to 2 in the divisor as well as next come 1 in the quotient. Step 5: find the remainder and also now drag down the pair of 0s indigenous the decimal part of the number. Dual the quotient to get the brand-new divisor. The new divisor is 34. Step 6: Repeat this procedure to gain the decimal locations you want.

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Therefore, the square source of 300 = 17.320

Prime Factorization

Next, this can be diminished further to300 = 22 × 3 × 52It is now easy to uncover the source from here:√300 = √(22 × 3 × 52)√300 = 10√3 = 17.320

Therefore, the square source of 300 ≅ 17.320

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Important Notes


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