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Square Root of 243

The square of 243 is a number which when multiplied with itself results in the number 243. The square root of any positive number is a real number while the square of every negative number is an imaginary number. Now, let’s calculate the square root of 243 using various methods and solve some interesting problems as well for better understanding.

Square root of 243: √243 = 15.58845
Square of 243: (243)²= 59049

1.	What Is the Square Root of 243?
2.	Is Square Root of 243 Rational or Irrational?
3.	How to Find the Square Root of 243?
4.	Important Notes on Square Root of 243
5.	FAQs on Square Root of 243

What is the Square Root of 243?

The square root of 243 in decimal form is 15.5884.
The square root of 243 is written as √243 in radical form.
The square root of 243 is written as (243)^1/3in exponential form.

Is Square Root of 243 Rational or Irrational?

A rational number is a number that can be written in the ratio of two integers p/q where q ≠ 0. We can’t write the square root of 243 in the form of p/q. Therefore, the square root of 243 is an irrational number.

How to Find the Square Root of 243?

Square Root of 243 Using Prime Factorization Method

Prime factorization of 243: 3⁵
Prime factors of 243 in pairs: (3 × 3) × (3× 3) × 3
Square root of 243: √243 = √((3× 3)²× 3) = (3× 3)√3 = 3√3

Square Root of 243 By Long Division

Start dividing the digits by drawing a line above them from the right side in pairs of two. In the case of 243, we have two pairs 43 and 2.
Now, find a number(y) whose square is ≤ 2. The value of y will be 1 as 1 × 1 = 1 ≤ 2.
We get the quotient and the remainder as 1. Now, add the divisor y with itself and get the new divisor 2y (2).
Bring down the next pair (new dividend becomes 124) and find a number (d) such that 2d × d ≤ 143. The value of n comes out to be 5.
Now, add a decimal in the dividend (243) and quotient (15) simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (243. 00 00 00) and repeat the above step for the remaining three pairs of zero.

So, we get the value of the square root of √243 = 15.588 by the long division method.

Square root of 243

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Important Notes:

The number 243 is not a perfect square.
The square root of 243 is an irrational number.
The square root of -243 is an imaginary number.

Example 1: By which smallest number 243 must be divided to make it a perfect square?

Solution:
To make 243 a perfect square we have to make the power of 3 an even number in the prime factorization of 243. And the prime factorization of 243 is 245 = 3⁵. So, to make it a perfect square we have to divide it by 3 then the power of 3 will be an even number.
Example 2: What the value of (4√243)/(√27)?

Solution:
The value of √243 = 9√3 and √27= 3√3
Therefore, (4√243)/√27 = (9 × 4√3)/ 3√3 = 12.

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FAQs on Square Roots of 243

What is the negative square root of 243?

The negative square root of 243 is -15.58845.

What is the square of 243?

The square of 243 is (243)³= 59049.

What is the prime factorization of 243?

The prime factorization of 243 is 245 = 3⁵.

Is the square root of 243 a rational number?

No, the square root of 243 is not a rational number because the square root of 243 can’t be expressed in p/q form.

Is the number 243 a perfect square?

No, 243 is not a perfect square because the square root of 243 is an irrational number.

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