**Finding square roots of perfect squares :**

Finding square roots is the opposite process squaring.

1² = 1, the square root of 1 is 1.

2² = 4, the square root of 4 is 2.

3² = 9, the square root of 9 is 3.

4² = 16, the square root of 16 is 4.

From the above example, we come to know that 16, 9, 4 and 1 are known as perfect squares. Because we can represent all as the multiples two same numbers.

That is 16 = 4 x 4, 9 = 3 x 3, 4 = 2 x 2, 1 = 1 x 1.

Like wise 18 is not a perfect square, because we cannot represent this 18 as the multiple of two same terms.

Usually we follow two methods to find square roots of perfect squares.

- Prime factorization method
- Long division method

Let us see some example problems to understand the method of finding square root using the above methods.

- Using this method, first we have to split the given number into prime factors.
- Write those prime factors inside the radical sign instead of the given number.
- Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.
- Multiply the numbers which have come out from the radical sign.

**Question 1 :**

Find the prime factors of 324

**Solution :**

**Step 1 :**

Since the given number ends with 4, first we have to split the given number by the smallest even prime number 2.

**Step 2 :**

2 goes into 3 one time.We have 1 left. If we take this 1 along with the next digit 2, we get 12. If we divide this by 2, we get 6.

We don’t have any number remaining in 12. So we can take the next digit 4. Again, if we divide 4 by 2, we get 2.

**Step 3 :**

√324 = √(2 x 2 x 3 x 3 x 3 x 3)

= 2 x 3 x 3

= 18

Hence the square square root of 324 is 18.

We can do the same problem using long division method

**Step 1 :**

Separate the digits by taking commas from right to left once in two digits.

3, 24

When we do so, we get 3 before the first comma.

**Step 2 :**

Now we have to multiply a number by itself such that

the product ≤ 3

(The product must be greatest and also less than 3)

The above condition will be met by “1”.

Because 1 x 1 = 1 ≤ 3, but 2 x 2 = 4 > 3

Now this situation is explained using long division

In the above picture, 1 is subtracted from 3 and we got the remainder 2.

**Step 3 :**

Now, we have to bring down 24 and quotient 1 to be multiplied by 2 as given in the picture below.

**Step 4 :**

Now we have to take a same number at the two places indicated by "?".

Then, we have to find the product as shown in the picture and also the product must meet the condition as indicated.

**Step 5 :**

The condition said in step 4 will be met by replacing "?" with "2".

Than we have to do the calculation as given in the picture.

Hence the square square root of 324 is 18.

**Question 2 :**

Find the prime factors of 625

**Solution :**

**Step 1 :**

Since the given number ends with 5, first we have to split it by the prime number 5.

**Step 2 :**

5 goes into 6 one time.We have 1 left. If we take this 1 along with the next digit 2, we get 12. Again we have to divide it by 5. If we divide this by 5, we get 2.

Now we have 2 left. Now we have to take this 2 along with the next digit 5, we get 25. If we divide 25 by 5, we get 5.

**Step 3 :**

By repeating this process until we get prime factors.

Hence, √625 = √(5 x 5 x 5 x 5) = 5 x 5 = 25

We can do the same problem using long division method

**Step 1 :**

Separate the digits by taking commas from right to left once in two digits.

3, 24

When we do so, we get 3 before the first comma.

**Step 2 :**

Now we have to multiply a number by itself such that

the product ≤ 6

(The product must be greatest and also less than 6)

The above condition will be met by “1”.

Because 2 x 2 = 4 ≤ 6, but 3 x 3 = 9 > 6

Now this situation is explained using long division

In the above picture, 4 is subtracted from 6 and we got the remainder 2.

**Step 3 :**

Now, we have to bring down 25 and quotient 1 to be multiplied by 2.

Now we have put a number next to 4, and the same number should be in the quotient next to 2. So that their product must be less than or equal to 225.

By multiplying 5 and 45, we will get the answer 225.

Hence 25 is the square root of 625.

After having gone through the stuff given above, we hope that the students would have understood "Square roots of perfect squares".

Apart from the stuff given above, if you want to know more about "Square roots of perfect squares", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**