Square Root of 195

The square root of 195 is expressed as √195 in the radical form and as (195)^½ or (195)^0.5 in the exponent form. The square root of 195 rounded up to 9 decimal places is 13.964240044. It is the positive solution of the equation x² = 195.

Square Root of 195: 13.96424004376894
Square Root of 195 in exponential form: (195)^½ or (195)^0.5
Square Root of 195 in radical form: √195

Square Root of 195

1.	What is the Square Root of 195?
2.	How to find the Square Root of 195?
3.	Is the Square Root of 195 Irrational?
4.	FAQs

What is the Square Root of 195?

The square root of 195, (or root 195), is the number which when multiplied by itself gives the product as 195. Therefore, the square root of 195 = √195 = 13.96424004376894.

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How to Find Square Root of 195?

Square Root of 195 by Long Division Method

Value of √195 by Long Division Method

Explanation:

Forming pairs: 01 and 95
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 95, to the right of the remainder 0. The new dividend is now 95.
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 3) such that 2Z × Z <= 95. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 95.
Divide 95 by 23 with the quotient as 3, giving the remainder = 95 - 23 × 3 = 95 - 69 = 26.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 26. The new dividend is now 2600.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 9) such that 26Z × Z <= 2600. Together they form a new divisor (269) for the new dividend (2600).
Divide 2600 by 269 with the quotient as 9, giving the remainder = 2600 - 269 × 9 = 2600 - 2421 = 179.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 195.

Therefore, the square root of 195 by long division method is 13.9 approx.

Is Square Root of 195 Irrational?

The actual value of √195 is undetermined. The value of √195 up to 25 decimal places is 13.96424004376894116988392. Hence, the square root of 195 is an irrational number.

☛ Also Check:

Square Root of 1521 - √1521 = 39
Square Root of 625 - √625 = 25
Square Root of 400 - √400 = 20
Square Root of 125 - √125 = 11.18034
Square Root of 1681 - √1681 = 41
Square Root of 33 - √33 = 5.74456
Square Root of 45 - √45 = 6.70820

Square Root of 195 Solved Examples

Example 1: Solve the equation x² − 195 = 0

Solution:

x² - 195 = 0 i.e. x² = 195
x = ±√195
Since the value of the square root of 195 is 13.964,
⇒ x = +√195 or -√195 = 13.964 or -13.964.
Example 2: If the area of a circle is 195π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 195π in²
⇒ r = ±√195 in
Since radius can't be negative,
⇒ r = √195
The square root of 195 is 13.964.
⇒ r = 13.964 in
Example 3: If the surface area of a cube is 1170 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 = 1170 in²
⇒ a = ±√195 in
Since length can't be negative,
⇒ a = √195
We know that the square root of 195 is 13.964.
⇒ a = 13.964 in

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FAQs on the Square Root of 195

What is the Value of the Square Root of 195?

The square root of 195 is 13.96424.

Why is the Square Root of 195 an Irrational Number?

Upon prime factorizing 195 i.e. 3¹ × 5¹ × 13¹, 3 is in odd power. Therefore, the square root of 195 is irrational.

If the Square Root of 195 is 13.964. Find the Value of the Square Root of 1.95.

Let us represent √1.95 in p/q form i.e. √(195/100) = 1.95/10 = 1.396. Hence, the value of √1.95 = 1.396

What is the Value of 2 square root 195?

The square root of 195 is 13.964. Therefore, 2 √195 = 2 × 13.964 = 27.928.

What is the Square Root of 195 in Simplest Radical Form?

We need to express 195 as the product of its prime factors i.e. 195 = 3 × 5 × 13. Therefore, as visible, the radical form of the square root of 195 cannot be simplified further. Therefore, the simplest radical form of the square root of 195 can be written as √195

What is the Square Root of -195?

The square root of -195 is an imaginary number. It can be written as √-195 = √-1 × √195 = i √195 = 13.964i
where i = √-1 and it is called the imaginary unit.

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