Square root of 88
2026-02-28 23:29 Diff
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Last updated on October 23, 2025

When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 88 Here 88 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.

What is the square root of 88?

The square root of 88 can be easily found out by using long division method. In which it is discovered that the cumulative approximation of √88 is 9.165.
 

Finding the square root of 88.

There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below.

Square root of 88 using the prime factorization method.

In this method, we decompose the number into its prime factors.


Prime factorization of 88: 88=2×2×2×11


Since not all prime factors can be paired, 88 cannot be simplified into a perfect square. Therefore, the square root of 88 cannot be expressed in a simple radical form.
 

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Square root of 88 using the division method.

For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:


Step 1: Write the number 88 to perform long division.


Step 2: Identify a perfect square number that is less than or equal to 88. For 88, that number is 81 (92).


Step 3: Divide 88 by 9. The remainder will be 7, and the quotient will be 9.


Step 4: Bring down the remainder (7) and append two zeros. Add a decimal point to the quotient, making it 9.0.


Step 5: Double the quotient to use as the new divisor, which gives 18.


Step 6: Select a number that, when multiplied by the new divisor, results in a product less than or equal to 700.


Step 7: Continue the division process to find √88 to the desired decimal places. → √88 ≈ 9.380.
 

Square root of 88 using the approximation method

In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.


Step 1: The nearest perfect squares to 88 are √100 = 10 and √81 = 9.


Step 2: Since 88 is between 100 and 81, we know the square root will be between 10 and 9.


Step 3: By testing numbers like 9.3, 9.4 and further, we find that √86 ≈ 9.380.
 

Common mistakes when finding the square root of 88.

Here are some common mistakes students should avoid while learning to calculate the square root of 88.
 

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Problem 1

What is the square root of a negative number like √-16?

Okay, lets begin

→The square root of √-16 is 4i
 

Explanation

Since √-16= √-16 × √-1, where √-1= i (i is an imaginary number). Hence, the square root of √-16 is 4i.
 

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Problem 2

Find x²+8, let x = √144.

Okay, lets begin

x=144 ≈ 12
x2=144
x2+8=144+8= 152
 

Explanation

Since √144 is equal to x and as we can see that x is square, hence when we square a root number it cancels out the root. Therefore, 144 + 8 = 152.
   

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Problem 3

Simplify √72 ÷ √8.

Okay, lets begin

= √72 ÷ √8


= √9


= 3
 

Explanation

Using the property of the division method, we get √9, and the square root of 9 is ±3.
.
 

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FAQs on the square root of 88.

1.How do you simplify 3√98?

3√98 can be simplified to 21√2, as we can express √98 as 7√2. 3 × 7 is equal to 21 hence it will be written as 21√2.
 

2. Is 88 a prime number?

No, If we use long division on 88 we get to know that it has divisors more than just 1 and itself, so it is not a prime number. It also has its own prime factors.
 

3.10 is the square root of what number?

 To find out what number 10 is the square root of, we need to multiply the number 10 with itself, the resulting number would be the answer in this case 10 × 10 is equal to 100.
 

4.What is the square root of 64?

By applying the long division method on 64 we get to know that 8 divides 64 to 0 using 8 meaning 8 × 8 is equal to 64, which makes 8 the square root of 64.
 

5.What is cube root?

The cube root of a number is a number which when obtained by multiplying it with itself three times gives the resultant of the initial number. For example, the cube root of 27 is 3 as 3 × 3 × 3 = 27.
 

Important Glossaries for Square Root of 88.

  • Square Root: A number which when is multiplied by itself gives the original number is called a square root.
  • Perfect Square: A number that is the integral square of an integer I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.
  • Prime Factorization: The ability to factorize a number in to the product of the basic arithmetic numbers, also known as primary numbers.
  • Non-Perfect Square: A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).
  • Approximation Method: Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated.

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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.

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