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Square Root of 166

The square root of 166 is expressed as √166 in the radical form and as (166)^½ or (166)^0.5 in the exponent form. The square root of 166 rounded up to 5 decimal places is 12.88410. It is the positive solution of the equation x² = 166.

Square Root of 166: 12.884098726725126
Square Root of 166 in exponential form: (166)^½ or (166)^0.5
Square Root of 166 in radical form: √166

Square Root of 166

1.	What is the Square Root of 166?
2.	How to find the Square Root of 166?
3.	Is the Square Root of 166 Irrational?
4.	FAQs

What is the Square Root of 166?

The square root of 166, (or root 166), is the number which when multiplied by itself gives the product as 166. Therefore, the square root of 166 = √166 = 12.884098726725126.

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How to Find Square Root of 166?

Square Root of 166 by Long Division Method

Value of √166 by Long Division Method

Explanation:

Forming pairs: 01 and 66
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 66, to the right of the remainder 0. The new dividend is now 66.
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 <= 66. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 66.
Divide 66 by 22 with the quotient as 2, giving the remainder = 66 - 22 × 2 = 66 - 44 = 22.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 22. The new dividend is now 2200.
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 <= 2200. Together they form a new divisor (248) for the new dividend (2200).
Divide 2200 by 248 with the quotient as 8, giving the remainder = 2200 - 248 × 8 = 2200 - 1984 = 216.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 166.

Therefore, the square root of 166 by long division method is 12.8 approx.

Is Square Root of 166 Irrational?

The actual value of √166 is undetermined. The value of √166 up to 25 decimal places is 12.88409872672512549464433. Hence, the square root of 166 is an irrational number.

☛ Also Check:

Square Root of 68 - √68 = 8.24621
Square Root of 900 - √900 = 30
Square Root of 136 - √136 = 11.66190
Square Root of 106 - √106 = 10.29563
Square Root of 240 - √240 = 15.49193
Square Root of 21 - √21 = 4.58258
Square Root of 54 - √54 = 7.34847

Square Root of 166 Solved Examples

Example 1: Solve the equation x² − 166 = 0

Solution:

x² - 166 = 0 i.e. x² = 166
x = ±√166
Since the value of the square root of 166 is 12.884,
⇒ x = +√166 or -√166 = 12.884 or -12.884.
Example 2: If the area of a circle is 166π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 166π in²
⇒ r = ±√166 in
Since radius can't be negative,
⇒ r = √166
The square root of 166 is 12.884.
⇒ r = 12.884 in
Example 3: If the surface area of a cube is 996 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 = 996 in²
⇒ a = ±√166 in
Since length can't be negative,
⇒ a = √166
We know that the square root of 166 is 12.884.
⇒ a = 12.884 in

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FAQs on the Square Root of 166

What is the Value of the Square Root of 166?

The square root of 166 is 12.88409.

Why is the Square Root of 166 an Irrational Number?

Upon prime factorizing 166 i.e. 2¹ × 83¹, 2 is in odd power. Therefore, the square root of 166 is irrational.

Is the number 166 a Perfect Square?

The prime factorization of 166 = 2¹ × 83¹. Here, the prime factor 2 is not in the pair. Therefore, 166 is not a perfect square.

If the Square Root of 166 is 12.884. Find the Value of the Square Root of 1.66.

Let us represent √1.66 in p/q form i.e. √(166/100) = 1.66/10 = 1.288. Hence, the value of √1.66 = 1.288

Evaluate 3 plus 15 square root 166

The given expression is 3 + 15 √166. We know that the square root of 166 is 12.884. Therefore, 3 + 15 √166 = 3 + 15 × 12.884 = 3 + 193.261 = 196.261

What is the Square of the Square Root of 166?

The square of the square root of 166 is the number 166 itself i.e. (√166)² = (166)^2/2 = 166.

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