Square Root of 353

The square root of 353 is irrational. The approximate value of the square root of 353 is 18.79. When an integer is multiplied by itself, the resultant product is termed as the perfect square number and the integer that was multiplied is termed as the square root of the product. A number “s” is a square root, when s × s or -s × -s gives a product p. “p” will be called the perfect square number and “s” its square root. 

Consider the number 19 × 19 = 361 and 18 × 18 = 324. 353 lies between 361 and 324. So the square root of 353 lies between 18 and 19 as 353 is not a perfect square number. Hence, the square root of 353 is also not a perfect integer. Therefore, √353 is an irrational number. You can refer to Square Root for a detailed explanation.

Note the Following:

• The Square root of 353 = √353 where ‘√’ is the radical, and 353 is the radicand.
• Exponential Form of Square root of 353 = 353^1/2
• Solution for √353 ≈ 18.79
• The square root of 353 is Irrational = True

What is the Square root of 353?

The square root of 353 is 18.79, as the square root of 353 is irrational.

How to Find the Square root of 353?

There are three methods to find the Square root of 353 

• Prime Factorisation method
• Long Division method
• Repeated Subtraction method

Square root of 353 by Prime Factorisation Method

In the prime factorisation method, the steps to find the square root of 353 is:

1. Divide 353 by prime factors. 

Since 353 is a prime number, it has no factors other than 1 and 353. 

353 = 353 × 1

This implies that 353 is not a perfect square number and has no perfect square root.

Therefore the square root of 353 = √353 = irrational = 18.78

Square root of 353 by Long Division Method

To understand the long division method, follow the below-mentioned detailed steps;

Step 1:  Grouping the given number into pairs. 

Step 2: Consider the first number, use the divisor such that the product is less than or equal to the first number. The divisors should be:

1 × 1 = 1 

2 × 2 = 4

3 × 3 = 9

Step 3: Continue the division, by bringing the next pair.

Step 4: The first divisor in the next division to be  (Divisor of first division + quotient of first division) such that:

d1 × 1 =

d2 × 2 =

d3 × 3 =

 And so on. 

Step 5: If the division is complete with the remainder as zero, then the quotient will be the square root. Else the number is not a perfect square number.

Applying the above steps to 353.

Groups are 3 and 13.

The squares are: 

1 × 1 = 1

2 × 2 = 4

Hence, 353 does not have a perfect square. Therefore 353 is an irrational number whose root lies between 18 and 19.

Square root of 353 by Repeated Subtraction Method.

In the repeated Subtraction method, 353 is subtracted with odd numbers starting with 1 and the results with 3, 5, 7 and so on. If the result at any point becomes zero, then the number is a perfect square and the step at which it becomes zero is the square root. 

The table below shows repeated subtraction for the given number 353. 

The result at step 19 becomes negative and not zero. Hence 353 is not a perfect square number. The square root of 353 lies between 18 and 19.

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Solved Examples

1. What needs to be added to 353 to get a perfect square number?

Solution: 8 needs to be added to 353 to make a sum of 361, which is a perfect square. The square root for 361 is 19.

2. Does 353 have a perfect square root?

Solution: No. 353 does not have a perfect square root.