Square root of 68 is the number which, once multiplied by itself, gives the product as 68. In this lesson, we will certainly calculate the square root of 68 by long department method in addition to finding the answers to the following questions:

Are all also numbers perfect squares?Is the square root of 68 irrational?Let us uncover the square root of 68.

You are watching: Square root of 68 in radical form

**Square Root of 68**:

**√**68 = 8.246

**Square of 68: 682**= 4624

1. | What Is the Square Root of 68? |

2. | Is Square Root of 68 Rational or Irrational? |

3. | How to Find the Square Root of 68? |

4. | Thinking Out of the Box! |

5. | FAQs on Square Root of 68 |

6. | Important Notes on Square Root of 68 |

7. | Challenging Questions |

## What Is the Square Root of 68?

Square root is just an inverse procedure of square.** **In the number presented listed below, 2 is the square root of 4, however 4 is a perfect square. Does that suppose that numbers that are not perfect squares cannot have a square root?

Non-square numbers can have actually a square root, however they will not be whole numbers.**The square root of 68 is represented as √**68. The **square root of 68** is the number which as soon as multiplied to itself gives us the result as 68.**Throughout prehistoric times, Greeks discovered a number that could not be composed in the create of p/q, wright here p, q are integers and also q ≠ 0.**

## Is the Square Root of 68 Rational or Irrational?

**A number that cannot be expressed as a ratio of 2 integers is an irrational number. The decimal develop of the irrational number will be non-terminating (i.e. it never before ends) and non-recurring (i.e. the decimal component of the number never repeats a pattern). Now let us look at the square root of 68.√**68 = 8.24621125124. Do you think the decimal component stops after 8.24621125124? No, it is never-finishing and also you cannot find a pattern in the decimal part. Therefore, the square root of 68 is an irrational number.

## How to Find the Square Root of 68?

We can find the square root of 68 utilizing miscellaneous methods.**1. Repeated Subtraction2. Prime Factorization3. Estimation and also Approximation4. Long Division**

**Square Root of 68 by Prime Factorization**

**Let"s attempt finding the square root of 68 using prime factorization.Prime factorization of 68 = 2 × 2 × 17As such, √**68 = **√**(2 × 2 × 17) = 2**√**17**2√**17 is in the lowest form and cannot be simplified additionally. Hence, we have actually expressed the square root of 68 in the radical create. Can you try and also expush the square root of 26 in a similar way?

### Square Root of 68 by Long Division Method

The worth of the square root of 68 by lengthy division approach consists of the adhering to steps.

**Tip 1:**Find the largest number whose square is less than or equal to the number 68. Take this number as the divisor and the quotient (8 in this case). Divide and also write the remainder.

**Step 2:**In the quotient, put a decimal point after 8. Bring down two zeroes to the best of the remainder. So, the brand-new dividfinish is 400.

**Step 3:**Double the divisor. Now a part of the divisor is 16. Think of a number whose product is incredibly close to 400 and also that is less than or equal to 400. 2 will be the following quotient. Now we acquire our brand-new divisor as 162, as 162 × 2 = 324. Do the department and also acquire the remainder.

**Step 4:**Repeat this procedure approximately three decimal areas.

Explore square roots using illustrations and also interactive examples

**Think Tank:**

Can you think of any kind of perfect square number after 68?Since (√(-68)2)= 68, have the right to we say that √(-68) is also a square root of 68?

**Challenging Questions:**

What is the worth of the square root of 682?Simplify ((

**√**68)½)½Determine the square root of 268.

See more: How Do Protons Determine The Bonding Properties Of An Atom Are Determined By Its

**Important Notes:**

The square root of 68 in the radical develop is expressed as

**√**68In exponent form, the square root of 68 is expressed as 68½The real roots of

**√**68 are ±8.24.