Last updated on May 26th, 2025
The square root of 9 is a value “y” such that when “y” is multiplied by itself → y × y, the result is 9. The number 9 has a unique non-negative square root, called the principal square root. Square root concept are applied in real life in the field of engineering, GPS and distance calculations, for scaling objects proportionally, etc.
The square root of 9 is ±3, where 3 is the positive solution of the equation x2 = 9. Finding the square root is just the inverse of squaring a number and hence, squaring 3 will result in 9. The square root of 9 is written as √9 in radical form, where the ‘√’ sign is called the “radical” sign. In exponential form, it is written as (9)1/2
We can find the square root of 9 through various methods. They are:
The prime factorization of 9 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore.
So, Prime factorization of 9 = 3 ×3
Square root of 9= √[3 × 3] = 3
This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 9:
Step 1: Write the number 9 and draw a bar above the pair of digits from right to left.
Step 2: Now, find the greatest number whose square is less than or equal to 9. Here, it is 3 because 32=9
Step 3: now divide 9 by 3 (the number we got from Step 2) such that we get 3 as a quotient, and we get a remainder 0.
Step 4: The quotient obtained is the square root of 9. In this case, it is 3.
We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:
Step 1: take the number 9 and then subtract the first odd number from it. Here, in this case, it is 9-1=8
Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 8, and again subtract the next odd number after 1, which is 3, → 8-3=5.
Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 3 steps.
So, the square root is equal to the count, i.e., the square root of 9 is ±3.
When we find the square root of 4, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.
Find √(4×9)×√(4×9)×√(4×9) ?
√(4×9)×√(4×9)×√(4×9)
= (4×9)×√(4×9)
= (4×9)×2×3
=216
Answer : 216
We found the values of the square roots of 4 and 9, then simplified the expression using square root concepts and multiplied the values.
What is √9 multiplied by 45 and then divided by 5 ?
√9 × 45/5
= 3×9
= 27
Answer: 27
finding the value of √9 and multiplying by 45/5.
A circular dish of radius equals to 3 meters. Find its area.
radius = 3 m
Area of a circle = π×(radius)2
⇒ Area of a circle = 3.14×(3)2
⇒ Area of a circle=3.14×9 = 28.26 sq. meters
Answer: The area of a circular dish is 28.26 sq. meters
Applying the formula for finding the area of a circle with a given radius.
Find the length of a side of a square whose area is 9 cm²
Given, the area = 9 cm2
We know that, (side of a square)2 = area of square
Or, (side of a square)2 = 9
Or, (side of a square)= √9
Or, the side of a square = ± 3.
But, the length of a square is a positive quantity only, so, the length of the side is 3 cm.
Answer: 3 cm
We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square
Find (√9 / √49) × (√36/√64)
(√9 / √49) × (√36/√64)
=(3/7)×(6/8)
= 9/28
Answer : 9/28
we firstly found out the values of √9, √49,√36 and √64 then solved .
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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