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Square Root of 353

The square root of 353 is expressed as √353 in the radical form and as (353)^½ or (353)^0.5 in the exponent form. The square root of 353 rounded up to 10 decimal places is 18.7882942281. It is the positive solution of the equation x² = 353.

Square Root of 353: 18.788294228055936
Square Root of 353 in exponential form: (353)^½ or (353)^0.5
Square Root of 353 in radical form: √353

Square Root of 353

1.	What is the Square Root of 353?
2.	How to find the Square Root of 353?
3.	Is the Square Root of 353 Irrational?
4.	FAQs

What is the Square Root of 353?

The square root of 353, (or root 353), is the number which when multiplied by itself gives the product as 353. Therefore, the square root of 353 = √353 = 18.788294228055936.

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How to Find Square Root of 353?

Square Root of 353 by Long Division Method

Value of √353 by Long Division Method

Explanation:

Forming pairs: 03 and 53
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 53, to the right of the remainder 2. The new dividend is now 253.
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 <= 253. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 253.
Divide 253 by 28 with the quotient as 8, giving the remainder = 253 - 28 × 8 = 253 - 224 = 29.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 29. The new dividend is now 2900.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 7) such that 36Z × Z <= 2900. Together they form a new divisor (367) for the new dividend (2900).
Divide 2900 by 367 with the quotient as 7, giving the remainder = 2900 - 367 × 7 = 2900 - 2569 = 331.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 353.

Therefore, the square root of 353 by long division method is 18.7 approximately.

Is Square Root of 353 Irrational?

The actual value of √353 is undetermined. The value of √353 up to 25 decimal places is 18.78829422805593599904520. Hence, the square root of 353 is an irrational number.

☛ Also Check:

Square Root of 25 - √25 = 5
Square Root of 37 - √37 = 6.08276
Square Root of 51 - √51 = 7.14143
Square Root of 56 - √56 = 7.48331
Square Root of 60 - √60 = 7.74597
Square Root of 289 - √289 = 17
Square Root of 49 - √49 = 7

Square Root of 353 Solved Examples

Example 1: Solve the equation x² − 353 = 0

Solution:

x² - 353 = 0 i.e. x² = 353
x = ±√353
Since the value of the square root of 353 is 18.788,
⇒ x = +√353 or -√353 = 18.788 or -18.788.
Example 2: If the surface area of a cube is 2118 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 2118 in²
⇒ a = ±√353 in
Since length can't be negative,
⇒ a = √353
We know that the square root of 353 is 18.788.
⇒ a = 18.788 in
Example 3: If the area of an equilateral triangle is 353√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 353√3 in²
⇒ a = ±√1412 in
Since length can't be negative,
⇒ a = √1412 = 2 √353
We know that the square root of 353 is 18.788.
⇒ a = 37.577 in

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FAQs on the Square Root of 353

What is the Value of the Square Root of 353?

The square root of 353 is 18.78829.

Why is the Square Root of 353 an Irrational Number?

The number 353 is prime. This implies that the number 353 is pairless and is not in the power of 2. Therefore, the square root of 353 is irrational.

Is the number 353 a Perfect Square?

The number 353 is prime. This implies that the square root of 353 cannot be expressed as a product of two equal integers. Therefore, the number 353 is not a perfect square.

What is the Square of the Square Root of 353?

The square of the square root of 353 is the number 353 itself i.e. (√353)² = (353)^2/2 = 353.

What is the Square Root of -353?

The square root of -353 is an imaginary number. It can be written as √-353 = √-1 × √353 = i √353 = 18.788i
where i = √-1 and it is called the imaginary unit.

Evaluate 6 plus 16 square root 353

The given expression is 6 + 16 √353. We know that the square root of 353 is 18.788. Therefore, 6 + 16 √353 = 6 + 16 × 18.788 = 6 + 300.613 = 306.613

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