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Square Root of 356

The square root of 356 is expressed as √356 in the radical form and as (356)^½ or (356)^0.5 in the exponent form. The square root of 356 rounded up to 10 decimal places is 18.8679622641. It is the positive solution of the equation x² = 356. We can express the square root of 356 in its lowest radical form as 2 √89.

Square Root of 356: 18.867962264113206
Square Root of 356 in exponential form: (356)^½ or (356)^0.5
Square Root of 356 in radical form: √356 or 2 √89

Square Root of 356

1.	What is the Square Root of 356?
2.	How to find the Square Root of 356?
3.	Is the Square Root of 356 Irrational?
4.	FAQs

What is the Square Root of 356?

The square root of 356, (or root 356), is the number which when multiplied by itself gives the product as 356. Therefore, the square root of 356 = √356 = 2 √89 = 18.867962264113206.

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How to Find Square Root of 356?

Square Root of 356 by Long Division Method

Value of √356 by Long Division Method

Explanation:

Forming pairs: 03 and 56
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 56, to the right of the remainder 2. The new dividend is now 256.
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 <= 256. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 256.
Divide 256 by 28 with the quotient as 8, giving the remainder = 256 - 28 × 8 = 256 - 224 = 32.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 32. The new dividend is now 3200.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 8) such that 36Z × Z <= 3200. Together they form a new divisor (368) for the new dividend (3200).
Divide 3200 by 368 with the quotient as 8, giving the remainder = 3200 - 368 × 8 = 3200 - 2944 = 256.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 356.

Therefore, the square root of 356 by long division method is 18.8 approximately.

Is Square Root of 356 Irrational?

The actual value of √356 is undetermined. The value of √356 up to 25 decimal places is 18.86796226411320762264132. Hence, the square root of 356 is an irrational number.

☛ Also Check:

Square Root of 12 - √12 = 3.46410
Square Root of 13 - √13 = 3.60555
Square Root of 11 - √11 = 3.31662
Square Root of 192 - √192 = 13.85641
Square Root of 17 - √17 = 4.12311
Square Root of 162 - √162 = 12.72792
Square Root of 1296 - √1296 = 36

Square Root of 356 Solved Examples

Example 1: Solve the equation x² − 356 = 0

Solution:

x² - 356 = 0 i.e. x² = 356
x = ±√356
Since the value of the square root of 356 is 18.868,
⇒ x = +√356 or -√356 = 18.868 or -18.868.
Example 2: If the area of an equilateral triangle is 356√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 = 356√3 in²
⇒ a = ±√1424 in
Since length can't be negative,
⇒ a = √1424 = 2 √356
We know that the square root of 356 is 18.868.
⇒ a = 37.736 in
Example 3: If the area of a circle is 356π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 356π in²
⇒ r = ±√356 in
Since radius can't be negative,
⇒ r = √356
The square root of 356 is 18.868.
⇒ r = 18.868 in

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FAQs on the Square Root of 356

What is the Value of the Square Root of 356?

The square root of 356 is 18.86796.

Why is the Square Root of 356 an Irrational Number?

Upon prime factorizing 356 i.e. 2² × 89¹, 89 is in odd power. Therefore, the square root of 356 is irrational.

Is the number 356 a Perfect Square?

The prime factorization of 356 = 2² × 89¹. Here, the prime factor 89 is not in the pair. Therefore, 356 is not a perfect square.

What is the Square Root of -356?

The square root of -356 is an imaginary number. It can be written as √-356 = √-1 × √356 = i √356 = 18.867i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 356?

The square of the square root of 356 is the number 356 itself i.e. (√356)² = (356)^2/2 = 356.

What is the Value of 13 square root 356?

The square root of 356 is 18.868. Therefore, 13 √356 = 13 × 18.868 = 245.284.

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