**Square roots :**

The square root of a number is the value such that, when a number multiplied by itself,for example

3 x 3 = 9

It is written with a radical symbol " √ " and the number or
expression inside the radical symbol is called the
radicand.

(ii) Long division method

- 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 square-root of 324 by prime factorization

**Solution :**

Step 1 :

Split 324 into prime factors

**Step 2 :**

√324 = √2 x 2 x 3 x 3 x 3 x 3

**Step 3 :**

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

Hence, square root of 324 is 18.

**Question 2 : **

Find square root of 625 by prime factorization

**Solution :**

Step 1 :

Split 625 into prime factors

**Step 2 :**

√625 = √5 x 5 x 5 x 5

**Step 3 :**

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

= 5 x 5

= 25

Hence, √625 is 25.

**Question 3 : **

Find square-root of 4096 by prime factorization

**Solution :**

**Step 1 :**

Split 625 into prime factors

**Step 2 :**

√4096 = √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

**Step 3 :**

Take one common number from the radical

= 2 x 2 x 2 x 2

= 64

Hence, square-root of 4096 is 64.

**Question 4 : **

Find square-root of 400 by prime factorization

**Solution :**

Step 1 :

Split 400 into prime factors

**Step 2 :**

√400 = √2 x 2 x 2 x 2 x 5 x 5

**Step 3 :**

= 2 x 2 x 5

= 20

Hence, square root of √400 is 20.

**Question 5 : **

Find square-root of 144 by prime factorization

**Solution :**

**Step 1 :**

Split 144 into prime factors

**Step 2 :**

√144 = √2 x 2 x 2 x 2 x 3 x 3

**Step 3 :**

= 2 x 2 x 3

= 12

Hence, √144 is 12.

**Question 6 : **

Find the square-root of 104976 by long division method

**Solution :**

**Step 1 :**

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

10,49,76

When we do so, we get 10 before the first comma.

**Step 2 :**

Now we have to multiply a number by itself such that

the product ≤ 10

(The product must be greatest and also less than 10)

The above condition will be met by “3”.

Because 3x3 = 9 ≤ 10

Now this situation is explained using long division

In the above picture, 9 is subtracted from 10 and we got the remainder 1.

**Step 3 :**

Now, we have to bring down 49 and quotient 3 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.

**Step 6 :**

Now, we have to bring down 76 and quotient 32 to be multiplied by 2 as given in the picture below.

**Step 7 :**

In the above picture, we have applied the procedures explained in step 4 and step 5. And we got the remainder zero.

**Step 8 :**

From the above picture, finally we got the square root of 104976. That is 324.

**Hence, the square root of 104976 = 324**

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

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

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

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the 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**