The square root of 312 is expressed as √312 in the radical kind and as (312)½ or (312)0.5 in the exponent form. The square source of 312 rounded up to 8 decimal areas is 17.66352173. That is the optimistic solution of the equation x2 = 312. We have the right to express the square root of 312 in its shortest radical form as 2 √78.

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Square source of 312: 17.663521732655695Square root of 312 in exponential form: (312)½ or (312)0.5Square root of 312 in radical form: √312 or 2 √78

 1 What is the Square root of 312? 2 How to uncover the Square root of 312? 3 Is the Square root of 312 Irrational? 4 FAQs

The square source of 312, (or source 312), is the number which once multiplied through itself gives the product together 312. Therefore, the square root of 312 = √312 = 2 √78 = 17.663521732655695.

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### Value the √312 by Long division Method

Explanation:

Forming pairs: 03 and 12Find a number Y (1) such the whose square is lug down the next pair 12, to the right of the remainder 2. The brand-new dividend is currently 212.Add the critical digit of the quotient (1) come the divisor (1) i.e. 1 + 1 = 2. Come the best of 2, uncover a number Z (which is 7) such that 2Z × Z division 212 through 27 through the quotient as 7, giving the remainder = 212 - 27 × 7 = 212 - 189 = 23.Now, let"s uncover the decimal places after the quotient 17.Bring down 00 to the best of this remainder 23. The new dividend is currently 2300.Add the critical digit the quotient come divisor i.e. 7 + 27 = 34. To the best of 34, uncover a digit Z (which is 6) such that 34Z × Z division 2300 by 346 with the quotient as 6, giving the remainder = 2300 - 346 × 6 = 2300 - 2076 = 224.Bring under 00 again. Repeat above steps for finding an ext decimal areas for the square root of 312.

Therefore, the square source of 312 by long department method is 17.6 approximately.

The actual worth of √312 is undetermined. The value of √312 as much as 25 decimal locations is 17.66352173265569370952809. Hence, the square root of 312 is an irrational number.

Example 1: deal with the equation x2 − 312 = 0

Solution:

x2 - 312 = 0 i.e. X2 = 312x = ±√312Since the value of the square root of 312 is 17.664,⇒ x = +√312 or -√312 = 17.664 or -17.664.

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## FAQs top top the Square root of 312

### What is the worth of the Square root of 312?

The square root of 312 is 17.66352.

### Why is the Square root of 312 an Irrational Number?

Upon prime factorizing 312 i.e. 23 × 31 × 131, 2 is in strange power. Therefore, the square root of 312 is irrational.

### What is the Square root of -312?

The square root of -312 is an imagine number. It have the right to be written as √-312 = √-1 × √312 = i √312 = 17.663iwhere i = √-1 and it is referred to as the imagine unit.

### What is the worth of 16 square source 312?

The square source of 312 is 17.664. Therefore, 16 √312 = 16 × 17.664 = 282.616.

### What is the Square that the Square root of 312?

The square that the square source of 312 is the number 312 chin i.e. (√312)2 = (312)2/2 = 312.

See more: 12 2/3 As An Improper Fraction, What Is 12/3 As A Mixed Number

### What is the Square source of 312 in simplest Radical Form?

We need to express 312 as the product the its prime factors i.e. 312 = 2 × 2 × 2 × 3 × 13. Therefore, √312 = √2 × 2 × 2 × 3 × 13 = 2 √78. Thus, the square root of 312 in the shortest radical form is 2 √78.