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 repetitive subtraction technique and settle a few interesting problems.

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Square source of 81: √81 = 9Square of 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 note on Square root of 81 5 Challenging Questions 6 FAQs on 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 also -9 can be expressed as 9/1 and also -9/1Both numbers have the right to be represented in the kind of a reasonable number.Hence, the square source of 81 is a rational number.

The square root of 81 have the right to be calculate using various methods such together prime administrate or the recurring subtraction method.

### Square root of 81 by repeated Subtraction Method

Start indigenous 81 and also keep individually the successive 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 subtracted 9 times to achieve 0. Thus, the square root of 81 is 9.

### Square source of 81 by element factorization method

Prime administer is express the number together a product the its element factors.The prime element of 81 is 3. 81 = 3 × 3 × 3 × 3The square source of 81 is √81 = √( 3 × 3 × 3 × 3)√81 = √( 9 × 9)(81½ )2 = ( 9 ½ )2Squaring top top both the sides, we gain 81 = 9

Explore Square roots using illustrations and interactive examples

The square root of 81 is expressed as √81 in the radical form and together 81½ in exponential form.The square root of 81 way the second root that 81 = +9 or -9The square source of only perfect squares can be calculated easily using the prime factorization method or repeated subtraction method. 81 is a perfect square.
Mike uses a ladder of length 15 feet and starts painting the wall. The foot that the ladder is 9 feet away. If the height of the wall from the floor is 12 feet, climate how much is the foot of the ladder native the ground?

Example 1: Sam has chose to plant 81 roses in his garden in together a method that every row contains as plenty of plants as the number of rows. Find the number of rows and also the variety of plants in every row.

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

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

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