Subscribe to our YouTube channel for the latest videos, updates, and tips.


Square Root of a Perfect Square by using the Prime Factorization Method



To find the square root of a perfect square by using the prime factorization method when a given number is a perfect square:

Step I: Resolve the given number into prime factors.

Step II: Make pairs of similar factors.

Step III: Take the product of prime factors, choosing one factor out of every pair.



Examples on square root of a perfect square by using the prime factorization method:

1. Find the square root of 484 by prime factorization method.

Solution:

Resolving 484 as the product of primes, we get

484 = 2 × 2 × 11 × 11 

√484 = √(2 × 2 × 11 × 11

= 2 × 11

Therefore, √484 = 22



2. Find the square root of 324.

Solution:


The square root of 324 by prime factorization, we get


324 = 2 × 2 × 3 × 3 × 3 × 3

√324 = √(2 × 2 × 3 × 3 × 3 × 3)

= 2 × 3 × 3


Therefore, √324 = 18



3. Find out the square root of 1764.

Solution:


The square root of 1764 by prime factorization, we get

1764 = 2 x 2 x 3 x 3 x 7 x 7.

√1764 = √(2 x 2 x 3 x 3 x 7 x 7)

= 2 x 3 x 7




Therefore, √1764 = 42.



4. Evaluate √4356

Solution:


By using prime factorization, we get

4356 = 2 x 2 x 3 x 3 x 11 x 11

√4356 = √(2 x 2 x 3 x 3 x 11 x 11)

= 2 × 3 × 11




Therefore, √4356 = 66.



5. Evaluate √11025

Solution:


By using prime factorization, we get

11025 = 5 x 5 x 3 x 3 x 7 x 7.

√11025 = √(5 x 5 x 3 x 3 x 7 x 7)

= 5 × 3 × 7





Therefore, √11025 = 105

6. In an auditorium, the number of rows is equal to the number of chairs in each row. If the capacity of the auditorium is 2025, find the number of chairs in each row.

Solution:


Let the number of chairs in each row be x.

Then, the number of rows = x.

Total number of chairs in the auditorium = (x × x) = x²

But, the capacity of the auditorium = 2025 (given).

Therefore, x² = 2025

= 5 × 5 × 3 × 3 × 3 × 3

x = (5 × 3 × 3) = 45.






Hence, the number of chairs in each row = 45


7. Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square.

Solution:


By prime factorization, we get

396 = 2 × 2 × 3 × 3 × 11

It is clear that in order to get a perfect square, one more 11 is required.

So, the given number should be multiplied by 11 to make the product a perfect square.




8. Find the smallest number by which 1100 must be divided so that the quotient is a perfect square.

Solution:


Expressing 1100 as the product of primes, we get

1100 = 2 × 2 × 5 × 5 × 11

Here, 2 and 5 occur in pairs and 11 does not.

Therefore, 1100 must be divided by 11 so that the quotient is 100

i.e., 1100 ÷ 11 = 100 and 100 is a perfect square.



9. Find the least square number divisible by each one of 8, 9and 10.

Solution:


The least number divisible by each one of 8, 9, 10 is their LCM.

Now, LCM of 8, 9, 10 = (2 × 4 × 9 × 5) = 360

By prime factorization, we get

360 = 2 × 2 × 2 × 3 × 3 × 5

To make it a perfect square it must be multiplied by (2 × 5) i.e., 10.





Hence, the required number = (360 × 10) = 3600.


 Square Root

Square Root

Square Root of a Perfect Square by using the Prime Factorization Method

Square Root of a Perfect Square by Using the Long Division Method

Square Root of Numbers in the Decimal Form

Square Root of Number in the Fraction Form

Square Root of Numbers that are Not Perfect Squares

Table of Square Roots

Practice Test on Square and Square Roots


● Square Root- Worksheets

Worksheet on Square Root using Prime Factorization Method

Worksheet on Square Root using Long Division Method

Worksheet on Square Root of Numbers in Decimal and Fraction Form











8th Grade Math Practice

From Square Root of a Perfect Square by using the Prime Factorization Method to HOME PAGE



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. How to Find the Average? | What Does Average Mean? | Definition

    May 15, 25 06:05 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  2. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More

  3. Worksheet on Rounding Decimals | Questions Related to Round a Decimal

    May 15, 25 11:52 AM

    Worksheet on Rounding Decimals
    The worksheet on rounding decimals would be really good for the students to practice huge number of questions related to round a decimal. This worksheet include questions related

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 14, 25 03:01 PM

    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Rounding Off to the Nearest Whole Number | Nearest 10, 100, and 1000

    May 13, 25 03:43 PM

    Nearest Ten
    Here we will learn how to rounding off to the nearest whole number?

    Read More