The square root of 81 is a number, which when multiplied by itself results in the number 81. The square root of 81 is a rational number as it can be expressed in the form of p/q. In this article, we are going to learn three different methods to find the square root of 81 such as prime factorization, repeated subtraction method and the long division method in detail.
What is the Square Root of 81?
The square root of 81 is a number, which when multiplied by itself and resulting in the number 81. The square root of 81 is symbolically expressed as √81.
Hence, √81 = √(Number × Number)
Thus, if we multiply the number 9 two times, we get the original value 81.
(i.e) √81 = √(9 × 9)
√81 = √(9)2
Now, remove square and square root, we get
√81 = ± 9
|
Square Root of 81: 9 |
|---|
Similarly, the simplest radical form of the square root of 81 is √81.
|
Square Root of 81 in Radical Form: √81. |
|---|
Square Root of 81 by Prime Factorization Method
To find the square root of 81 using the prime factorization method, one must know the prime factorization of 81. We know that the prime factorization of 81 is 3 × 3 × 3 × 3.
Thus, √81 = √[3×3×3×3]
√81 = √[(3×3)×(3×3)]
This can also be written as
√81 = √(3)2. √(3)2
√81 = 3×3 = 9.
Hence, the value of the square root of 81 is 9.
Square Root of 81 by Repeated Subtraction Method
In this method, start from 81 and keep subtracting the successive odd number until we get the result 0. The total number of odd numbers we subtract is the square root of 81. Now, let us discuss how to find the square root of 81 using the repeated subtraction method.
81 – 1 = 80
80 – 3 = 77
77 – 5 = 72
72 – 7 = 65
65 – 9 = 56
56 – 11 = 45
45 – 13 = 32
32 – 15 = 17
17 – 17 = 0
Hence, starting from 81, we have subtracted 9 times to get the result 0. Hence, the square root of 81 is 9.
Square Root of 81 by Long Division Method
Follow the below steps to find the square root of 81 using the long division method:
Step 1: Write the number 81. Now, pair the number 81 from right to left by putting the bar on the top of the number.
Step 2: Now, divide the number 81 by a number, such that the product of the same number should be less than or equal to 81. Thus, 9×9 =81, which is equal to 81. Thus, we obtained the quotient = 9 and remainder = 0.
Step 3:Therefore, the value of the square root of 81, √81 is 9.
| Learn More on Square Root of a Number: |
|---|
Video Lessons on Square Roots
Visualising square roots
Finding Square roots
Examples
Example 1:
Simplify √81 + 9
Solution:
Given: √81 + 9
We know that the value of the square root of 81 is 9. Now, substitute the value in the above-given expression, we get
√81 +9 = 9+9
√81+9 = 18.
Hence, the simplified form of √81 +9 is 18.
Example 2:
Find the value of k, if 2√81 + k = 28.
Solution:
Given: 2√81 + k = 28.
We know that √81 = 9.
Now, substitute the value in the above equation, we get
2(9) +k = 28
18 + k = 28
k = 28 -18
k = 10.
Practice Questions
- What is the value of 15 plus square root of 81?
- Simplify (10√81) + 10.
- Find the value of a, if a√81 + 40 = 130
Stay tuned with BYJU’S – The Learning App and download the app to learn all Maths-related concepts by exploring more videos.
Frequently Asked Questions
What is the value of the square root of 81?
The value of the square root of 81 is 9.
Can we find the square root of 81 using the repeated subtraction method?
Yes, we can find the square root of 81 using the repeated subtraction method.
Is the square root of 81 a rational number?
Yes, the square root of 81 is a rational number since the value of the square root of 81 can be expressed in the form of 9/1
Is the number 81 a perfect square?
Yes, the number 81 is a perfect square. (i.e) 92 = 81.
What is the value of the square of square root of 81?
The value of square of the square root of 81 is 81.
(i.e.) (√81)2 = 81
Comments