Square Root of 168
The square root of 168 is expressed as √168 in the radical form and as (168)^{½} or (168)^{0.5} in the exponent form. The square root of 168 rounded up to 6 decimal places is 12.961481. It is the positive solution of the equation x^{2} = 168. We can express the square root of 168 in its lowest radical form as 2 √42.
 Square Root of 168: 12.96148139681572
 Square Root of 168 in exponential form: (168)^{½} or (168)^{0.5}
 Square Root of 168 in radical form: √168 or 2 √42
1.  What is the Square Root of 168? 
2.  How to find the Square Root of 168? 
3.  Is the Square Root of 168 Irrational? 
4.  FAQs 
What is the Square Root of 168?
The square root of 168, (or root 168), is the number which when multiplied by itself gives the product as 168. Therefore, the square root of 168 = √168 = 2 √42 = 12.96148139681572.
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How to Find Square Root of 168?
Value of √168 by Long Division Method
Explanation:
 Forming pairs: 01 and 68
 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 68, to the right of the remainder 0. The new dividend is now 68.
 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 <= 68. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 68.
 Divide 68 by 22 with the quotient as 2, giving the remainder = 68  22 × 2 = 68  44 = 24.
 Now, let's find the decimal places after the quotient 12.
 Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
 Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 9) such that 24Z × Z <= 2400. Together they form a new divisor (249) for the new dividend (2400).
 Divide 2400 by 249 with the quotient as 9, giving the remainder = 2400  249 × 9 = 2400  2241 = 159.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 168.
Therefore, the square root of 168 by long division method is 12.9 approx.
Is Square Root of 168 Irrational?
The actual value of √168 is undetermined. The value of √168 up to 25 decimal places is 12.96148139681572046193193. Hence, the square root of 168 is an irrational number.
☛ Also Check:
 Square Root of 196  √196 = 14
 Square Root of 1681  √1681 = 41
 Square Root of 250  √250 = 15.81139
 Square Root of 289  √289 = 17
 Square Root of 136  √136 = 11.66190
 Square Root of 16  √16 = 4
 Square Root of 125  √125 = 11.18034
Square Root of 168 Solved Examples

Example 1: Solve the equation x^{2} − 168 = 0
Solution:
x^{2}  168 = 0 i.e. x^{2} = 168
x = ±√168
Since the value of the square root of 168 is 12.961,
⇒ x = +√168 or √168 = 12.961 or 12.961. 
Example 2: If the area of an equilateral triangle is 168√3 in^{2}. 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)a^{2} = 168√3 in^{2}
⇒ a = ±√672 in
Since length can't be negative,
⇒ a = √672 = 2 √168
We know that the square root of 168 is 12.961.
⇒ a = 25.923 in 
Example 3: If the area of a square is 168 in^{2}. 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 = a^{2} = 168 in^{2}
⇒ a = ±√168 in
Since length can't be negative,
⇒ a = √168 = 12.961 in
FAQs on the Square Root of 168
What is the Value of the Square Root of 168?
The square root of 168 is 12.96148.
Why is the Square Root of 168 an Irrational Number?
Upon prime factorizing 168 i.e. 2^{3} × 3^{1} × 7^{1}, 2 is in odd power. Therefore, the square root of 168 is irrational.
What is the Square Root of 168 in Simplest Radical Form?
We need to express 168 as the product of its prime factors i.e. 168 = 2 × 2 × 2 × 3 × 7. Therefore, √168 = √2 × 2 × 2 × 3 × 7 = 2 √42. Thus, the square root of 168 in the lowest radical form is 2 √42.
What is the Value of 9 square root 168?
The square root of 168 is 12.961. Therefore, 9 √168 = 9 × 12.961 = 116.653.
Evaluate 19 plus 13 square root 168
The given expression is 19 + 13 √168. We know that the square root of 168 is 12.961. Therefore, 19 + 13 √168 = 19 + 13 × 12.961 = 19 + 168.499 = 187.499
If the Square Root of 168 is 12.961. Find the Value of the Square Root of 1.68.
Let us represent √1.68 in p/q form i.e. √(168/100) = 1.68/10 = 1.296. Hence, the value of √1.68 = 1.296