Square root of 68 is the number which, when multiplied by itself, gives the product as 68. In this lesson, we will calculate the square root of 68 by long division method along with finding the answers to the following questions:

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

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**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 operation of square.** **In the figure shown below, 2 is the square root of 4, but 4 is a perfect square. Does that mean that numbers that are not perfect squares cannot have a square root?

Non-square numbers can have a square root, but they will not be whole numbers.**The square root of 68 is represented as √**68. The **square root of 68** is the number which when multiplied to itself gives us the result as 68.**During ancient times, Greeks found a number that could not be written in the form of p/q, where p, q are integers and q ≠ 0.**

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

**A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of the irrational number will be non-terminating (i.e. it never ends) and non-recurring (i.e. the decimal part 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 part stops after 8.24621125124? No, it is never-ending and you cannot find a pattern in the decimal part. Thus, 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 using various methods.**1. Repeated Subtraction2. Prime Factorization3. Estimation and Approximation4. Long Division**

**Square Root of 68 by Prime Factorization**

**Let"s try finding the square root of 68 using prime factorization.Prime factorization of 68 = 2 × 2 × 17Therefore, √**68 = **√**(2 × 2 × 17) = 2**√**17**2√**17 is in the lowest form and cannot be simplified further. Thus, we have expressed the square root of 68 in the radical form. Can you try and express the square root of 26 in a similar way?

### Square Root of 68 by Long Division Method

The value of the square root of 68 by long division method consists of the following steps.

**Step 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 write the remainder.

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

**Step 3:**Double the divisor. Now a part of the divisor is 16. Think of a number whose product is very close to 400 and that is less than or equal to 400. 2 will be the next quotient. Now we get our new divisor as 162, as 162 × 2 = 324. Do the division and get the remainder.

**Step 4:**Repeat this process up to three decimal places.

Explore square roots using illustrations and interactive examples

**Think Tank:**

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

**Challenging Questions:**

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

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

See more: How Many Moles Of Copper Are Equivalent To 3.44 × 1023 Atoms Of Copper?

**Important Notes:**

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

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

**√**68 are ±8.24.