261 LearnersLast updated on May 26th, 2025
Square root of 162
Let’s discuss what is a square root? The square root of a number is a number, when multiplied by itself gives the number. Radical symbol (√) is the symbol used to indicate square root. The square root of 25 is ±5. We use it in our daily life in physics, engineering, finance etc.
What is the square root of 162
In this topic, the square root of 162 is ±12.72. The square root of 162 is expressed as √162, in radical form. It is expressed as (162)½ in exponential form.
Finding the square root of 162
If a student wants to find the square root of a number. Which are the methods they can use? Some common methods are,
- Prime factorization
- Long division
- Approximation
- Subtraction method
Let’s check the square root of 162 using these methods
Square root of 162 by prime factorization
In this method, all the prime factors of the number are listed down and then from there one number from each pair is listed down. Then the numbers are multiplied together.
By using prime factorization, let’s check out the square root of 162.
Step 1: Listing out the prime factors of 162 and pairing the same numbers.
Prime factors of 162 = 2 × 3 × 3 × 3 × 3
Pairing the factors i.e, 2 × (3 × 3), (3 × 3)
Step 2: multiplying a number from each pair
√2 × 3 × 3 = 9√2
Hence, the √162 is 9√2
Square root of 162 by long division
Using the long division method, let’s check the square root of 162
Step 1: The number given, 162 has three digits so let’s pair that number. Here it is 1 and 62.
Finding the number whose square is less than or equal to the 1
Here the number is, because 12 = 1
Step 2: So, let’s divide 1 by 1
Step 3: Now, the quotient and divisor is 1, for the new divisor we add the divisor with itself.
Step 4: Continue the process till the remainder is 0
The quotient will be the square root of the number.
Therefore, the square root of 162 is ±12.727
Square root of 162 by approximation
Approximation method is mainly used for not a perfect square. As 162 is not a perfect square, the approximation method can be used to find the square root of 162.
Step 1: Find any two perfect squares numbers between which 162 lies. The two perfect squares are 122 (144) and 132 (169)
Therefore, the square root of 162 lies between 12 and 13, i.e, 12 < √162 <13
Step 2: for checking out the decimal part, the formula is
given number - lower perfect square / bigger perfect square - lowest perfect square
Hence,162 - 144 /169 - 144 = 18 / 25 = 0.72
So, the approximate square of 162 is 12. 72
Square root of 162 by subtraction method
In the subtraction method, based on the fact, the sum of the first n odd number is n2. So, here the given number is subtracted with the odd number starting with 1. The process will go on till the given number becomes 0. The method is mainly used for perfect squares; it is not used to find the square root of 162.
Common errors and how to avoid them in the square root of 162
Students tend to make errors while finding the square root of a number. So, let’s check some common errors while finding the square root and the ways to avoid it
Mistake 1
Errors while counting the prime factors
Students tend to make errors in the prime factorization method by making errors in counting. To avoid it, make sure to recount each factor. And make sure to verify the answer.
Square root of 162 examples
Problem 1
The length of sides of a right-angled triangle is 9 and √162 units. Find the length of the hypotenuse? If a = 9 and b = √162
According to Pythagorean theorem, c = √a2 + b2
Hence, c2 = a2 + b2
C2 = 92 + √1622 = 81 + 162 = 243
C2 = 243
C = √243 = 9√3
Explanation
To find the length of hypotenuse of a right angle triangle we need to use Pythagorean theorem, c = √a2 + b2
Problem 2
Calculate the value of 3/√162?
The value of √162 is 12.72
So, 3 / √162 = 3 / 12.72 = 0.236
The vale of 3/√162 = 0.236
Explanation
use the value of √162 = 12.72
Problem 3
If the radius of a circle is √162, calculate the circumference of the circle?
The circumference of a circle = 2πr
Here, r = √162
The value of √162 = 12.72
So, 2πr = 2 × 3.14 × 12.72 = 79.882
Explanation
Therefore, the circumference of the circle is 79.882
Problem 4
If ABCD is a rectangle, the length of AB and CD is √162, the length of AC and BD is 3. Find the length of AD?
The length of rectangle = √162
The width of a rectangle = 3
The length of diagonal = x
The line, AD, divided the rectangle into 2 right angle triangles.
So length of AD = √AB + CD (Pythagorean theorem)
So AD2 = AB2 + CD2
AD2 = (√162)2 + 32
= 162 + 9 = 171
AD = √171
Explanation
The diagonal of the rectangle divides it into two right-angled triangles. So, the length of the diagonal of the rectangle is the length of the hypotenuse triangle.
FAQs on 162 square root
1.Write the simplest form of √162?
2.Is √162 value a rational or irrational number?
3.List out the factors of 162?
4.Find the value of √162 + √162
5.Check whether 161 is a perfect square?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square root of 162?
8.How do technology and digital tools in Thailand support learning Algebra and Square root of 162?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important glossaries for square root of 162
- Quotient: The result we got after dividing two numbers is the quotient
- Radical symbol: The radical symbol (√) is the symbol used to denote square root.
- Square of a number: The Square of a number is the product of the number when multiplied by itself.
- Prime factorization: It is the process of breaking down a number into prime numbers.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
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