81 is a perfect square number and it is the fourth power the 3. I.e. ( 34 ). In this lesson, we will calculate the square source of 81 by recurring subtraction method and solve a couple of interesting problems.

You are watching: What is the square root of negative 81

**Square root of 81**: √81 = 9

**Square that 81: 81² =**6,561

1. | What Is the Square source of 81? |

2. | Is Square source of 81 reasonable or Irrational? |

3. | How to find the Square source of 81? |

4. | Important note on Square root of 81 |

5. | Challenging Questions |

6. | FAQs ~ above Square root of 81 |

81 = a × a = a2 Thus, a = √81= √(9 × 9)9 × 9 = 81 or -9 × -9 = 81. Therefore √81= ± 9This shows that 81 is a perfect square.

9 and -9 have the right to be expressed as 9/1 and also -9/1Both numbers can be represented in the type of a rational number.Hence, the square root of 81 is a reasonable number.

The square source of 81 can be calculation using different methods such together prime administer or the recurring subtraction method.

### Square source of 81 by recurring Subtraction Method

Start from 81 and also keep individually the succeeding odd number till we achieve zero. The complete numbers we subtract is the square source of 81.

81 - 1 = 8080 - 3 = 7777 - 5 = 7272 - 7 = 6565 - 9 = 5656 -11 = 4545 -13 = 3232 -15 = 1717 - 17 = 0Thus beginning from 81, we have actually subtracted 9 time to acquire 0. Thus, the square source of 81 is 9.

### Square root of 81 by prime factorization method

Prime administer is expressing the number as a product the its element factors.The prime aspect of 81 is 3. 81 = 3 × 3 × 3 × 3The square root of 81 is √81 = √( 3 × 3 × 3 × 3)√81 = √( 9 × 9)(81½ )2 = ( 9 ½ )2Squaring top top both the sides, we obtain 81 = 9Explore Square roots making use of illustrations and interactive examples

The square root of 81 is expressed together √81 in the radical type and together 81½ in exponential form.The square root of 81 way the second root that 81 = +9 or -9The square source of just perfect squares have the right to be calculated quickly using the prime factorization method or repetitive subtraction method. 81 is a perfect square.

Mike provides a ladder of size 15 feet and starts painting the wall. The foot the the ladder is 9 feet away. If the elevation of the wall surface from the floor is 12 feet, climate how far is the foot the the ladder from the ground?

**Example 1: **Sam has decided to tree 81 roses in his garden in together a way that every row includes as plenty of plants as the number of rows. Find the number of rows and the variety of plants in every row.

**Solution:**Number of** **rows × variety of rose plants = 81 climbed plantsGiven the the variety of rows = the number of plants = nn × n = 81 n2 = 81n = ± 9 Rows and plants space numbered in hopeful only.Therefore, Sam have the right to have 9 rows the 9 rose plants each.

See more: What Is 39/45 As A Percentage, Convert Fraction (Ratio) 39 / 45 Answer: 86

**Example 2: **Danio finds a square digital picture on a website. The image consisted of 810,000 pixels. Just how high is the picture in pixels?

**Solution: **

The pixels occupied by the photo = area that the square picture = 810,000 pixels.The size or height of the picture = side of the squareside × side = 810000side = √ 810000= (81 × 10000)½= (92 × 1002)½= (9 × 100) = 900 pixels

Get answer >

go to slidego to slide

Want to construct a strong foundation in Math?

Go beyond memorizing formulas and also understand the ‘why’ behind them. Experience charline-picon.com and get started.