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Square Root of 352

The square root of 352 is expressed as √352 in the radical form and as (352)^½ or (352)^0.5 in the exponent form. The square root of 352 rounded up to 9 decimal places is 18.761663039. It is the positive solution of the equation x² = 352. We can express the square root of 352 in its lowest radical form as 4 √22.

Square Root of 352: 18.76166303929372
Square Root of 352 in exponential form: (352)^½ or (352)^0.5
Square Root of 352 in radical form: √352 or 4 √22

Square Root of 352

1.	What is the Square Root of 352?
2.	How to find the Square Root of 352?
3.	Is the Square Root of 352 Irrational?
4.	FAQs

What is the Square Root of 352?

The square root of 352, (or root 352), is the number which when multiplied by itself gives the product as 352. Therefore, the square root of 352 = √352 = 4 √22 = 18.76166303929372.

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How to Find Square Root of 352?

Square Root of 352 by Long Division Method

Value of √352 by Long Division Method

Explanation:

Forming pairs: 03 and 52
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 52, to the right of the remainder 2. The new dividend is now 252.
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 <= 252. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 252.
Divide 252 by 28 with the quotient as 8, giving the remainder = 252 - 28 × 8 = 252 - 224 = 28.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 28. The new dividend is now 2800.
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 <= 2800. Together they form a new divisor (367) for the new dividend (2800).
Divide 2800 by 367 with the quotient as 7, giving the remainder = 2800 - 367 × 7 = 2800 - 2569 = 231.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 352.

Therefore, the square root of 352 by long division method is 18.7 approximately.

Is Square Root of 352 Irrational?

The actual value of √352 is undetermined. The value of √352 up to 25 decimal places is 18.76166303929371821826252. Hence, the square root of 352 is an irrational number.

☛ Also Check:

Square Root of 120 - √120 = 10.95445
Square Root of 324 - √324 = 18
Square Root of 75 - √75 = 8.66025
Square Root of 77 - √77 = 8.77496
Square Root of 44 - √44 = 6.63325
Square Root of 96 - √96 = 9.79796
Square Root of 73 - √73 = 8.54400

Square Root of 352 Solved Examples

Example 1: Solve the equation x² − 352 = 0

Solution:

x² - 352 = 0 i.e. x² = 352
x = ±√352
Since the value of the square root of 352 is 18.762,
⇒ x = +√352 or -√352 = 18.762 or -18.762.
Example 2: If the area of a circle is 352π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 352π in²
⇒ r = ±√352 in
Since radius can't be negative,
⇒ r = √352
The square root of 352 is 18.762.
⇒ r = 18.762 in
Example 3: If the area of a square is 352 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 = 352 in²
⇒ a = ±√352 in
Since length can't be negative,
⇒ a = √352 = 18.762 in

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FAQs on the Square Root of 352

What is the Value of the Square Root of 352?

The square root of 352 is 18.76166.

Why is the Square Root of 352 an Irrational Number?

Upon prime factorizing 352 i.e. 2⁵ × 11¹, 2 is in odd power. Therefore, the square root of 352 is irrational.

If the Square Root of 352 is 18.762. Find the Value of the Square Root of 3.52.

Let us represent √3.52 in p/q form i.e. √(352/100) = 3.52/10 = 1.876. Hence, the value of √3.52 = 1.876

What is the Square of the Square Root of 352?

The square of the square root of 352 is the number 352 itself i.e. (√352)² = (352)^2/2 = 352.

What is the Value of 14 square root 352?

The square root of 352 is 18.762. Therefore, 14 √352 = 14 × 18.762 = 262.663.

What is the Square Root of 352 in Simplest Radical Form?

We need to express 352 as the product of its prime factors i.e. 352 = 2 × 2 × 2 × 2 × 2 × 11. Therefore, √352 = √2 × 2 × 2 × 2 × 2 × 11 = 4 √22. Thus, the square root of 352 in the lowest radical form is 4 √22.

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