81 is a perfect square number and also it is the 4th power that 3. I.e. ( 34 ). In this lesson, we will calculate the square source of 81 by repeated subtraction an approach and resolve a couple of interesting problems.

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

Square source of 81: √81 = 9Square the 81: 81² = 6,561
 1 What Is the Square root of 81? 2 Is Square root of 81 rational or Irrational? 3 How to find the Square root of 81? 4 Important notes 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 reflects that 81 is a perfect square.

9 and -9 can be expressed as 9/1 and -9/1Both numbers have the right to be stood for in the form of a reasonable number.Hence, the square source of 81 is a rational number.

The square source of 81 deserve to be calculate using various methods such together prime factorization or the repetitive subtraction method.

### Square root of 81 by repetitive Subtraction Method

Start from 81 and keep subtracting the succeeding odd number till we obtain zero. The complete numbers we subtract is the square root of 81.

81 - 1 = 8080 - 3 = 7777 - 5 = 7272 - 7 = 6565 - 9 = 5656 -11 = 4545 -13 = 3232 -15 = 1717 - 17 = 0

Thus starting from 81, we have actually subtracted 9 times to achieve 0. Thus, the square source of 81 is 9.

### Square source of 81 by prime factorization method

Prime factorization is expressing the number as a product of its element factors.The prime element 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 acquire 81 = 9

Explore Square roots using illustrations and interactive examples

The square source of 81 is expressed together √81 in the radical type and as 81½ in exponential form.The square source of 81 method the second root of 81 = +9 or -9The square root of just perfect squares can be calculated quickly using the prime factorization an approach or repetitive subtraction method. 81 is a perfect square.
Mike supplies a ladder of size 15 feet and also starts painting the wall. The foot the the ladder is 9 feet away. If the height of the wall from the floor is 12 feet, then how far is the foot the the ladder indigenous the ground?

Example 1: Sam has determined to tree 81 roses in his garden in together a method that each row has as many plants as the variety of rows. Find the variety of rows and also the variety of plants in every row.

Solution:Number of rows × variety of rose plants = 81 rose plantsGiven the the variety of rows = the variety of plants = nn × n = 81 n2 = 81n = ± 9 Rows and plants are numbered in positive only.Therefore, Sam deserve to have 9 rows of 9 increased plants each.

See more: What Is The Hardest Word To Guess In Hangman ? 40 Hardest Words To Guess In Hangman

Example 2: Danio finds a square digital picture on a website. The image included 810,000 pixels. How high is the photo in pixels?

Solution:

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