204 LearnersLast updated on May 26th, 2025
Square root of 176
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 176
In this article, the square root of 176 is ±13.26. The square root of 176 is expressed as √176, in radical form. It is expressed as (176)½ in exponential form.
Finding the square root of 176
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 176 using these methods
Square root of 176 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 176.
Step 1: Listing out the prime factors of 176 and pairing the same numbers.
Prime factors of 176 = 2 × 2 × 2 × 2 × 11
Pairing the factors, i.e, (2 × 2) × (2 × 2) × 11
Step 2: multiplying a number from each pair
2 × 2 ×√11 = 4√11
Hence, the √176 is 4√11
Square root of 176 by long division
Here, the given number is divided into smaller numbers to find the square root of the number.
Using the long division method, let’s check the square root of 176
Step 1: The number given, 176 has three digits so let’s pair that number. Here it is 1 and 75.
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 176 is ±13.266
Square root of 176 by approximation
Approximation method is mainly used for not a perfect square. As 176 is not a perfect square, the approximation method can be used to find the square root of 176.
Step 1: Find any two perfect squares numbers between which 176 lies. The two perfect squares are 132 (169)and 142 (196)
Therefore, the square root of 176 lies between 13 and 14, i.e, 13 < √176 <14
Step 2: for checking out the decimal part, the formula is
Hence,176 - 169/ 196 - 169 = 7/27 = 0.259
So, the approximate square of 176 is ±13.259
Square root of 176 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 176.
Common errors and how to avoid them in the square root of 176
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 176 examples
Problem 1
If the value of x in x² = 176
X2 = 176
In other words, x = ±√176
Explanation
or we can write the actual value of 13.26
Problem 2
The length of two sides of a right triangle is 6 and √170 units. Find the length of the longest side.
In right-angled triangle, c2 = a2 + b2
C2 = 62 + (170)2
C2 = 36+ 170
C = √206
Explanation
length of langest side is C = √206
Problem 3
which is smaller, √176 or √196
The smallest is √176
Explanation
Because √176 is ±13.26 whereas √169 is ±14, hence, √176 is smaller than √169
Problem 4
Find the product of 4√176 The value of √176 is ±4√11
The value of √176 is ±4√11
4 × 4√11 = 16√11
Explanation
the product of 4 × 4√11 = 16√11
FAQs on square root of 176
1.What goes into 176 evenly?
2.What is the greatest factor of 176?
3.Is 176 divisible by 8?
4.What is the prime factorization tree of 176
5.How does learning Algebra help students in Philippines make better decisions in daily life?
6.How can cultural or local activities in Philippines support learning Algebra topics such as Square root of 176?
7.How do technology and digital tools in Philippines support learning Algebra and Square root of 176?
8.Does learning Algebra support future career opportunities for students in Philippines?
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
: He loves to play the quiz with kids through algebra to make kids love it.
