The square source of 174 is expressed together √174 in the radical type and together (174)½ or (174)0.5 in the exponent form. The square source of 174 rounded up to 8 decimal areas is 13.19090596. That is the hopeful solution of the equation x2 = 174.

You are watching: What is the square root of 174 1 What is the Square source of 174? 2 How to discover the Square root of 174? 3 Is the Square source of 174 Irrational? 4 FAQs

☛ Check: Square source Calculator ### Value the √174 through Long department Method

Explanation:

Forming pairs: 01 and also 74Find a number Y (1) such that whose square is carry down the following pair 74, to the best of the remainder 0. The brand-new dividend is now 74.Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the appropriate of 2, find a number Z (which is 3) such the 2Z × Z divide 74 by 23 v the quotient as 3, offering the remainder = 74 - 23 × 3 = 74 - 69 = 5.Now, let"s uncover the decimal areas after the quotient 13.Bring under 00 come the appropriate of this remainder 5. The new dividend is currently 500.Add the critical digit that quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a number Z (which is 1) such that 26Z × Z divide 500 through 261 through the quotient together 1, offering the remainder = 500 - 261 × 1 = 500 - 261 = 239.Bring under 00 again. Repeat over steps for finding much more decimal areas for the square source of 174.

Therefore, the square source of 174 through long division method is 13.1 approx.

☛ likewise Check:

Example 1: resolve the equation x2 − 174 = 0

Solution:

x2 - 174 = 0 i.e. X2 = 174x = ±√174Since the worth 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 in2. Uncover the radius of the circle.

Solution:

Let "r" it is in the radius the the circle.⇒ Area that the one = πr2 = 174π in2⇒ r = ±√174 inSince radius can"t be negative,⇒ r = √174The square root of 174 is 13.191.⇒ r = 13.191 in

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## FAQs top top the Square source of 174

### What is the worth of the Square source of 174?

The square source of 174 is 13.1909.

### Why is the Square source of 174 one Irrational Number?

Upon prime factorizing 174 i.e. 21 × 31 × 291, 2 is in odd power. Therefore, the square root of 174 is irrational.

### What is the Square the the Square root of 174?

The square of the square source of 174 is the number 174 itself i.e. (√174)2 = (174)2/2 = 174.

### Evaluate 3 plus 13 square source 174

The given expression is 3 + 13 √174. We know that the square source of 174 is 13.191. Therefore, 3 + 13 √174 = 3 + 13 × 13.191 = 3 + 171.482 = 174.482

### If the Square source of 174 is 13.191. Discover the worth of the Square source of 1.74.See more: On The Record: Who Sang The Original Mr Grinch, You'Re A Mean One, Mr

Let us stand for √1.74 in p/q type i.e. √(174/100) = 1.74/10 = 1.319. Hence, the worth of √1.74 = 1.319

### What is the Square source of -174?

The square root of -174 is an imaginary number. It can be written as √-174 = √-1 × √174 = i √174 = 13.19iwhere ns = √-1 and also it is called the imaginary unit.