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

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

You are watching: Square root of 68 in radical form

**Square root of 68**:

**√**68 = 8.246

**Square the 68: 682**= 4624

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

2. | Is Square source of 68 rational or Irrational? |

3. | How to discover the Square source of 68? |

4. | Thinking out of the Box! |

5. | FAQs on Square source of 68 |

6. | Important note on Square source of 68 |

7. | Challenging Questions |

## What Is the Square source of 68?

Square source is simply an inverse procedure of square.** **In the figure displayed below, 2 is the square root of 4, however 4 is a perfect square. Go that mean that numbers that space not perfect squares cannot have a square root?

Non-square numbers have the right to have a square root, yet they will not be whole numbers.**The square root of 68 is represented as √**68. The **square root of 68** is the number which once multiplied come itself gives us the result as 68.**During old times, Greeks discovered a number that can not be written in the kind of p/q, whereby p, q room integers and also q ≠ 0.**

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

**A number that cannot be expressed as a proportion of 2 integers is an irrational number. The decimal type of the irrational number will certainly be non-terminating (i.e. It never ever ends) and non-recurring (i.e. The decimal part of the number never ever repeats a pattern). Now let us look in ~ the square source of 68.√**68 = 8.24621125124. Carry out you think the decimal component stops after ~ 8.24621125124? No, that is never-ending and also you cannot find a sample in the decimal part. Thus, the square source of 68 is one irrational number.

## How to uncover the Square root of 68?

We can discover the square source of 68 using assorted methods.**1. Repetitive Subtraction2. Element Factorization3. Estimation and Approximation4. Long Division**

**Square source of 68 by prime Factorization**

**Let"s try finding the square source of 68 using prime factorization.Prime administrate of 68 = 2 × 2 × 17Therefore, √**68 = **√**(2 × 2 × 17) = 2**√**17**2√**17 is in the lowest type and can not be streamlined further. Thus, we have actually expressed the square source of 68 in the radical form. Can you shot and to express the square root of 26 in a comparable way?

### Square root of 68 by Long department Method

The worth of the square source of 68 by long division method is composed of the complying with steps.

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

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

**Step 3:**Double the divisor. Currently a part of the divisor is 16. Think that a number whose product is an extremely close come 400 and also that is much less than or same to 400. 2 will certainly be the following quotient. Now we get our brand-new divisor as 162, as 162 × 2 = 324. Execute the division and obtain the remainder.

**Step 4:**Repeat this process up to 3 decimal places.

Explore square roots utilizing illustrations and also interactive examples

**Think Tank:**

Can friend think of any perfect square number after ~ 68?Since (√(-68)2)= 68, have the right to we say the √(-68) is likewise a square root of 68?

**Challenging Questions:**

What is the value of the square source 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 source of 68 in the radical kind is expressed together

**√**68In exponent form, the square source of 68 is expressed together 68½The genuine roots of

**√**68 are ±8.24.