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Square Root of 388

The square root of 388 is expressed as √388 in the radical form and as (388)^½ or (388)^0.5 in the exponent form. The square root of 388 rounded up to 5 decimal places is 19.69772. It is the positive solution of the equation x² = 388. We can express the square root of 388 in its lowest radical form as 2 √97.

Square Root of 388: 19.697715603592208
Square Root of 388 in exponential form: (388)^½ or (388)^0.5
Square Root of 388 in radical form: √388 or 2 √97

Square Root of 388

1.	What is the Square Root of 388?
2.	How to find the Square Root of 388?
3.	Is the Square Root of 388 Irrational?
4.	FAQs

What is the Square Root of 388?

The square root of 388, (or root 388), is the number which when multiplied by itself gives the product as 388. Therefore, the square root of 388 = √388 = 2 √97 = 19.697715603592208.

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How to Find Square Root of 388?

Square Root of 388 by Long Division Method

Value of √388 by Long Division Method

Explanation:

Forming pairs: 03 and 88
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 88, to the right of the remainder 2. The new dividend is now 288.
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 <= 288. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 288.
Divide 288 by 29 with the quotient as 9, giving the remainder = 288 - 29 × 9 = 288 - 261 = 27.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 6) such that 38Z × Z <= 2700. Together they form a new divisor (386) for the new dividend (2700).
Divide 2700 by 386 with the quotient as 6, giving the remainder = 2700 - 386 × 6 = 2700 - 2316 = 384.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 388.

Therefore, the square root of 388 by long division method is 19.6 approximately.

Is Square Root of 388 Irrational?

The actual value of √388 is undetermined. The value of √388 up to 25 decimal places is 19.69771560359220944349242. Hence, the square root of 388 is an irrational number.

☛ Also Check:

Square Root of 289 - √289 = 17
Square Root of 23 - √23 = 4.79583
Square Root of 40 - √40 = 6.32456
Square Root of 12 - √12 = 3.46410
Square Root of 99 - √99 = 9.94987
Square Root of 54 - √54 = 7.34847
Square Root of 45 - √45 = 6.70820

Square Root of 388 Solved Examples

Example 1: Solve the equation x² − 388 = 0

Solution:

x² - 388 = 0 i.e. x² = 388
x = ±√388
Since the value of the square root of 388 is 19.698,
⇒ x = +√388 or -√388 = 19.698 or -19.698.
Example 2: If the area of a square is 388 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 = 388 in²
⇒ a = ±√388 in
Since length can't be negative,
⇒ a = √388 = 19.698 in
Example 3: If the area of a circle is 388π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 388π in²
⇒ r = ±√388 in
Since radius can't be negative,
⇒ r = √388
The square root of 388 is 19.698.
⇒ r = 19.698 in

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FAQs on the Square Root of 388

What is the Value of the Square Root of 388?

The square root of 388 is 19.69771.

Why is the Square Root of 388 an Irrational Number?

Upon prime factorizing 388 i.e. 2² × 97¹, 97 is in odd power. Therefore, the square root of 388 is irrational.

If the Square Root of 388 is 19.698. Find the Value of the Square Root of 3.88.

Let us represent √3.88 in p/q form i.e. √(388/100) = 3.88/10 = 1.970. Hence, the value of √3.88 = 1.970

What is the Square of the Square Root of 388?

The square of the square root of 388 is the number 388 itself i.e. (√388)² = (388)^2/2 = 388.

What is the Square Root of -388?

The square root of -388 is an imaginary number. It can be written as √-388 = √-1 × √388 = i √388 = 19.697i
where i = √-1 and it is called the imaginary unit.

Is the number 388 a Perfect Square?

The prime factorization of 388 = 2² × 97¹. Here, the prime factor 97 is not in the pair. Therefore, 388 is not a perfect square.

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