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Square Root of 396

The square root of 396 is expressed as √396 in the radical form and as (396)^½ or (396)^0.5 in the exponent form. The square root of 396 rounded up to 7 decimal places is 19.8997487. It is the positive solution of the equation x² = 396. We can express the square root of 396 in its lowest radical form as 6 √11.

Square Root of 396: 19.8997487421324
Square Root of 396 in exponential form: (396)^½ or (396)^0.5
Square Root of 396 in radical form: √396 or 6 √11

Square Root of 396

1.	What is the Square Root of 396?
2.	How to find the Square Root of 396?
3.	Is the Square Root of 396 Irrational?
4.	FAQs

What is the Square Root of 396?

The square root of 396, (or root 396), is the number which when multiplied by itself gives the product as 396. Therefore, the square root of 396 = √396 = 6 √11 = 19.8997487421324.

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How to Find Square Root of 396?

Square Root of 396 by Long Division Method

Value of √396 by Long Division Method

Explanation:

Forming pairs: 03 and 96
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 96, to the right of the remainder 2. The new dividend is now 296.
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 9) such that 2Z × Z <= 296. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 296.
Divide 296 by 29 with the quotient as 9, giving the remainder = 296 - 29 × 9 = 296 - 261 = 35.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 35. The new dividend is now 3500.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 8) such that 38Z × Z <= 3500. Together they form a new divisor (388) for the new dividend (3500).
Divide 3500 by 388 with the quotient as 8, giving the remainder = 3500 - 388 × 8 = 3500 - 3104 = 396.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 396.

Therefore, the square root of 396 by long division method is 19.8 approx.

Is Square Root of 396 Irrational?

The actual value of √396 is undetermined. The value of √396 up to 25 decimal places is 19.89974874213239909468960. Hence, the square root of 396 is an irrational number.

☛ Also Check:

Square Root of 51 - √51 = 7.14143
Square Root of 113 - √113 = 10.63015
Square Root of 900 - √900 = 30
Square Root of 17 - √17 = 4.12311
Square Root of 125 - √125 = 11.18034
Square Root of 74 - √74 = 8.60233
Square Root of 54 - √54 = 7.34847

Square Root of 396 Solved Examples

Example 1: Solve the equation x² − 396 = 0

Solution:

x² - 396 = 0 i.e. x² = 396
x = ±√396
Since the value of the square root of 396 is 19.900,
⇒ x = +√396 or -√396 = 19.900 or -19.900.
Example 2: If the area of a square is 396 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 396 in²
⇒ a = ±√396 in
Since length can't be negative,
⇒ a = √396 = 19.900 in
Example 3: If the area of an equilateral triangle is 396√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 = 396√3 in²
⇒ a = ±√1584 in
Since length can't be negative,
⇒ a = √1584 = 2 √396
We know that the square root of 396 is 19.900.
⇒ a = 39.799 in

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FAQs on the Square Root of 396

What is the Value of the Square Root of 396?

The square root of 396 is 19.89974.

Why is the Square Root of 396 an Irrational Number?

Upon prime factorizing 396 i.e. 2² × 3² × 11¹, 11 is in odd power. Therefore, the square root of 396 is irrational.

What is the Square Root of 396 in Simplest Radical Form?

We need to express 396 as the product of its prime factors i.e. 396 = 2 × 2 × 3 × 3 × 11. Therefore, √396 = √2 × 2 × 3 × 3 × 11 = 6 √11. Thus, the square root of 396 in the lowest radical form is 6 √11.

Is the number 396 a Perfect Square?

The prime factorization of 396 = 2² × 3² × 11¹. Here, the prime factor 11 is not in the pair. Therefore, 396 is not a perfect square.

Evaluate 19 plus 2 square root 396

The given expression is 19 + 2 √396. We know that the square root of 396 is 19.900. Therefore, 19 + 2 √396 = 19 + 2 × 19.900 = 19 + 39.799 = 58.799

What is the Value of 1 square root 396?

The square root of 396 is 19.900. Therefore, 1 √396 = 1 × 19.900 = 19.900.

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