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Square Root of 336

The square root of 336 is expressed as √336 in the radical form and as (336)^½ or (336)^0.5 in the exponent form. The square root of 336 rounded up to 9 decimal places is 18.330302780. It is the positive solution of the equation x² = 336. We can express the square root of 336 in its lowest radical form as 4 √21.

Square Root of 336: 18.33030277982336
Square Root of 336 in exponential form: (336)^½ or (336)^0.5
Square Root of 336 in radical form: √336 or 4 √21

Square Root of 336

1.	What is the Square Root of 336?
2.	How to find the Square Root of 336?
3.	Is the Square Root of 336 Irrational?
4.	FAQs

What is the Square Root of 336?

The square root of 336, (or root 336), is the number which when multiplied by itself gives the product as 336. Therefore, the square root of 336 = √336 = 4 √21 = 18.33030277982336.

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How to Find Square Root of 336?

Square Root of 336 by Long Division Method

Value of √336 by Long Division Method

Explanation:

Forming pairs: 03 and 36
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 36, to the right of the remainder 2. The new dividend is now 236.
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 <= 236. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 236.
Divide 236 by 28 with the quotient as 8, giving the remainder = 236 - 28 × 8 = 236 - 224 = 12.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 12. The new dividend is now 1200.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 3) such that 36Z × Z <= 1200. Together they form a new divisor (363) for the new dividend (1200).
Divide 1200 by 363 with the quotient as 3, giving the remainder = 1200 - 363 × 3 = 1200 - 1089 = 111.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 336.

Therefore, the square root of 336 by long division method is 18.3 approximately.

Is Square Root of 336 Irrational?

The actual value of √336 is undetermined. The value of √336 up to 25 decimal places is 18.33030277982336002635219. Hence, the square root of 336 is an irrational number.

☛ Also Check:

Square Root of 85 - √85 = 9.21954
Square Root of 15 - √15 = 3.87298
Square Root of 324 - √324 = 18
Square Root of 90 - √90 = 9.48683
Square Root of 27 - √27 = 5.19615
Square Root of 34 - √34 = 5.83095
Square Root of 22 - √22 = 4.69042

Square Root of 336 Solved Examples

Example 1: Solve the equation x² − 336 = 0

Solution:

x² - 336 = 0 i.e. x² = 336
x = ±√336
Since the value of the square root of 336 is 18.330,
⇒ x = +√336 or -√336 = 18.330 or -18.330.
Example 2: If the area of a square is 336 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 = 336 in²
⇒ a = ±√336 in
Since length can't be negative,
⇒ a = √336 = 18.330 in
Example 3: If the surface area of a cube is 2016 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 = 2016 in²
⇒ a = ±√336 in
Since length can't be negative,
⇒ a = √336
We know that the square root of 336 is 18.330.
⇒ a = 18.330 in

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FAQs on the Square Root of 336

What is the Value of the Square Root of 336?

The square root of 336 is 18.3303.

Why is the Square Root of 336 an Irrational Number?

Upon prime factorizing 336 i.e. 2⁴ × 3¹ × 7¹, 3 is in odd power. Therefore, the square root of 336 is irrational.

Evaluate 16 plus 10 square root 336

The given expression is 16 + 10 √336. We know that the square root of 336 is 18.330. Therefore, 16 + 10 √336 = 16 + 10 × 18.330 = 16 + 183.303 = 199.303

What is the Square Root of 336 in Simplest Radical Form?

We need to express 336 as the product of its prime factors i.e. 336 = 2 × 2 × 2 × 2 × 3 × 7. Therefore, √336 = √2 × 2 × 2 × 2 × 3 × 7 = 4 √21. Thus, the square root of 336 in the lowest radical form is 4 √21.

What is the Square of the Square Root of 336?

The square of the square root of 336 is the number 336 itself i.e. (√336)² = (336)^2/2 = 336.

What is the Value of 20 square root 336?

The square root of 336 is 18.330. Therefore, 20 √336 = 20 × 18.330 = 366.606.

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