The square root of 189 is expressed as √189 in the radical form and together (189)½ or (189)0.5 in the exponent form. The square source of 189 rounded up to 7 decimal places is 13.7477271. It is the confident solution that the equation x2 = 189. We deserve to express the square root of 189 in its shortest radical type as 3 √21.

You are watching: What is the square root of 189

Square root of 189: 13.74772708486752Square source of 189 in exponential form: (189)½ or (189)0.5Square root of 189 in radical form: √189 or 3 √21 1 What is the Square root of 189? 2 How to find the Square root of 189? 3 Is the Square root of 189 Irrational? 4 FAQs

The square source of 189, (or root 189), is the number which once multiplied through itself provides the product together 189. Therefore, the square source of 189 = √189 = 3 √21 = 13.74772708486752.

☛ Check: Square root Calculator ### Value of √189 by Long division Method

Explanation:

Forming pairs: 01 and 89Find a number Y (1) such the whose square is lug down the next pair 89, to the appropriate of the remainder 0. The new dividend is now 89.Add the last digit that the quotient (1) come the divisor (1) i.e. 1 + 1 = 2. To the appropriate of 2, uncover a digit Z (which is 3) such that 2Z × Z division 89 through 23 with the quotient as 3, offering the remainder = 89 - 23 × 3 = 89 - 69 = 20.Now, let's uncover the decimal areas after the quotient 13.Bring down 00 come the ideal of this remainder 20. The new dividend is currently 2000.Add the critical digit of quotient come divisor i.e. 3 + 23 = 26. To the ideal of 26, find a number Z (which is 7) such the 26Z × Z divide 2000 by 267 v the quotient as 7, providing the remainder = 2000 - 267 × 7 = 2000 - 1869 = 131.Bring under 00 again. Repeat above steps for finding more decimal places for the square source of 189.

Therefore, the square source of 189 by long division method is 13.7 approximately.

Example 1: fix the equation x2 − 189 = 0

Solution:

x2 - 189 = 0 i.e. X2 = 189x = ±√189Since the value of the square root of 189 is 13.748,⇒ x = +√189 or -√189 = 13.748 or -13.748.

Show equipment >

go to slidego to slidego to slide Ready to see the world through math’s eyes?
Math is in ~ the core of everything we do. Reap solving real-world math problems in live classes and also become an professional at everything.

## FAQs top top the Square root of 189

### What is the value of the Square source of 189?

The square root of 189 is 13.74772.

### Why is the Square root of 189 one Irrational Number?

Upon element factorizing 189 i.e. 33 × 71, 3 is in odd power. Therefore, the square root of 189 is irrational.

### What is the Square source of -189?

The square root of -189 is an imagine number. It have the right to be written as √-189 = √-1 × √189 = i √189 = 13.747iwhere ns = √-1 and also it is dubbed the imaginary unit.

### What is the worth of 2 square source 189?

The square source of 189 is 13.748. Therefore, 2 √189 = 2 × 13.748 = 27.495.

### What is the Square root of 189 in most basic Radical Form?

We should express 189 together the product the its prime factors i.e. 189 = 3 × 3 × 3 × 7. Therefore, √189 = √3 × 3 × 3 × 7 = 3 √21. Thus, the square source of 189 in the shortest radical kind is 3 √21.