Square Root of 174
The square root of 174 is expressed as √174 in the radical form and as (174)^{½} or (174)^{0.5} in the exponent form. The square root of 174 rounded up to 8 decimal places is 13.19090596. It is the positive solution of the equation x^{2} = 174.
 Square Root of 174: 13.19090595827292
 Square Root of 174 in exponential form: (174)^{½} or (174)^{0.5}
 Square Root of 174 in radical form: √174
1.  What is the Square Root of 174? 
2.  How to find the Square Root of 174? 
3.  Is the Square Root of 174 Irrational? 
4.  FAQs 
What is the Square Root of 174?
The square root of 174, (or root 174), is the number which when multiplied by itself gives the product as 174. Therefore, the square root of 174 = √174 = 13.19090595827292.
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How to Find Square Root of 174?
Value of √174 by Long Division Method
Explanation:
 Forming pairs: 01 and 74
 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 74, to the right of the remainder 0. The new dividend is now 74.
 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 <= 74. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 74.
 Divide 74 by 23 with the quotient as 3, giving the remainder = 74  23 × 3 = 74  69 = 5.
 Now, let's find the decimal places after the quotient 13.
 Bring down 00 to the right of this remainder 5. The new dividend is now 500.
 Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 1) such that 26Z × Z <= 500. Together they form a new divisor (261) for the new dividend (500).
 Divide 500 by 261 with the quotient as 1, giving the remainder = 500  261 × 1 = 500  261 = 239.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 174.
Therefore, the square root of 174 by long division method is 13.1 approx.
Is Square Root of 174 Irrational?
The actual value of √174 is undetermined. The value of √174 up to 25 decimal places is 13.19090595827291917093681. Hence, the square root of 174 is an irrational number.
☛ Also Check:
 Square Root of 96  √96 = 9.79796
 Square Root of 30  √30 = 5.47723
 Square Root of 37  √37 = 6.08276
 Square Root of 99  √99 = 9.94987
 Square Root of 34  √34 = 5.83095
 Square Root of 324  √324 = 18
 Square Root of 74  √74 = 8.60233
Square Root of 174 Solved Examples

Example 1: Solve the equation x^{2} − 174 = 0
Solution:
x^{2}  174 = 0 i.e. x^{2} = 174
x = ±√174
Since the value of the square root of 174 is 13.191,
⇒ x = +√174 or √174 = 13.191 or 13.191. 
Example 2: If the area of a circle is 174π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 174π in^{2}
⇒ r = ±√174 in
Since radius can't be negative,
⇒ r = √174
The square root of 174 is 13.191.
⇒ r = 13.191 in 
Example 3: If the surface area of a cube is 1044 in^{2}. 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 = 6a^{2} = 1044 in^{2}
⇒ a = ±√174 in
Since length can't be negative,
⇒ a = √174
We know that the square root of 174 is 13.191.
⇒ a = 13.191 in
FAQs on the Square Root of 174
What is the Value of the Square Root of 174?
The square root of 174 is 13.1909.
Why is the Square Root of 174 an Irrational Number?
Upon prime factorizing 174 i.e. 2^{1} × 3^{1} × 29^{1}, 2 is in odd power. Therefore, the square root of 174 is irrational.
What is the Square of the Square Root of 174?
The square of the square root of 174 is the number 174 itself i.e. (√174)^{2} = (174)^{2/2} = 174.
Evaluate 3 plus 13 square root 174
The given expression is 3 + 13 √174. We know that the square root of 174 is 13.191. Therefore, 3 + 13 √174 = 3 + 13 × 13.191 = 3 + 171.482 = 174.482
If the Square Root of 174 is 13.191. Find the Value of the Square Root of 1.74.
Let us represent √1.74 in p/q form i.e. √(174/100) = 1.74/10 = 1.319. Hence, the value of √1.74 = 1.319
What is the Square Root of 174?
The square root of 174 is an imaginary number. It can be written as √174 = √1 × √174 = i √174 = 13.19i
where i = √1 and it is called the imaginary unit.