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Square Root of 165

The square root of 165 is expressed as √165 in the radical form and as (165)^½ or (165)^0.5 in the exponent form. The square root of 165 rounded up to 10 decimal places is 12.8452325787. It is the positive solution of the equation x² = 165.

Square Root of 165: 12.84523257866513
Square Root of 165 in exponential form: (165)^½ or (165)^0.5
Square Root of 165 in radical form: √165

Square Root of 165

1.	What is the Square Root of 165?
2.	How to find the Square Root of 165?
3.	Is the Square Root of 165 Irrational?
4.	FAQs

What is the Square Root of 165?

The square root of 165, (or root 165), is the number which when multiplied by itself gives the product as 165. Therefore, the square root of 165 = √165 = 12.84523257866513.

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How to Find Square Root of 165?

Square Root of 165 by Long Division Method

Value of √165 by Long Division Method

Explanation:

Forming pairs: 01 and 65
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 65, to the right of the remainder 0. The new dividend is now 65.
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 2) such that 2Z × Z <= 65. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 65.
Divide 65 by 22 with the quotient as 2, giving the remainder = 65 - 22 × 2 = 65 - 44 = 21.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 21. The new dividend is now 2100.
Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 8) such that 24Z × Z <= 2100. Together they form a new divisor (248) for the new dividend (2100).
Divide 2100 by 248 with the quotient as 8, giving the remainder = 2100 - 248 × 8 = 2100 - 1984 = 116.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 165.

Therefore, the square root of 165 by long division method is 12.8 approximately.

Is Square Root of 165 Irrational?

The actual value of √165 is undetermined. The value of √165 up to 25 decimal places is 12.84523257866512902011690. Hence, the square root of 165 is an irrational number.

☛ Also Check:

Square Root of 48 - √48 = 6.92820
Square Root of 240 - √240 = 15.49193
Square Root of 60 - √60 = 7.74597
Square Root of 106 - √106 = 10.29563
Square Root of 29 - √29 = 5.38516
Square Root of 42 - √42 = 6.48074
Square Root of 1521 - √1521 = 39

Square Root of 165 Solved Examples

Example 1: Solve the equation x² − 165 = 0

Solution:

x² - 165 = 0 i.e. x² = 165
x = ±√165
Since the value of the square root of 165 is 12.845,
⇒ x = +√165 or -√165 = 12.845 or -12.845.
Example 2: If the surface area of a sphere is 660π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 660π in²
⇒ r = ±√165 in
Since radius can't be negative,
⇒ r = √165
The square root of 165 is 12.845.
⇒ r = 12.845 in
Example 3: If the area of an equilateral triangle is 165√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 = 165√3 in²
⇒ a = ±√660 in
Since length can't be negative,
⇒ a = √660 = 2 √165
We know that the square root of 165 is 12.845.
⇒ a = 25.690 in

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FAQs on the Square Root of 165

What is the Value of the Square Root of 165?

The square root of 165 is 12.84523.

Why is the Square Root of 165 an Irrational Number?

Upon prime factorizing 165 i.e. 3¹ × 5¹ × 11¹, 3 is in odd power. Therefore, the square root of 165 is irrational.

What is the Square of the Square Root of 165?

The square of the square root of 165 is the number 165 itself i.e. (√165)² = (165)^2/2 = 165.

What is the Square Root of 165 in Simplest Radical Form?

We need to express 165 as the product of its prime factors i.e. 165 = 3 × 5 × 11. Therefore, as visible, the radical form of the square root of 165 cannot be simplified further. Therefore, the simplest radical form of the square root of 165 can be written as √165

What is the Value of 15 square root 165?

The square root of 165 is 12.845. Therefore, 15 √165 = 15 × 12.845 = 192.678.

Is the number 165 a Perfect Square?

The prime factorization of 165 = 3¹ × 5¹ × 11¹. Here, the prime factor 3 is not in the pair. Therefore, 165 is not a perfect square.

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