**Square roots of fractions and decimals :**

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.

- To find the square root of a fraction, we have to take separate square roots for both numerator and denominator.
- After taking square roots of both numerator and denominator separately, we can combine them.

- To find the square root of a decimal number, first we have to remove the decimal by multiplying the numerator and denominator by the multiples of 10.
- According to the given number, we have to decide whether the number to be multiplied by 10, 100 or 1000 etc in order to remove the decimal point.
- After removing the decimal point, we will get a fraction and now we have to take separate square roots.

Let us see some examples based on the above concepts.

**Example 1 :**

Find the square root of the following decimal number

2.56

**Solution :**

Since we have two numbers after the decimal point, we have to multiply both numerator and denominator by 100.

√2.56 = √2.56 x (100/100)

= √(256/100)

Now take separate square roots for both numerator and denominator. = √(256/100) = √256/√100 √256 = √(2x2x2x2x2x2x2x2) √100 = √(2x2x5x5) |

√256 = 2 x 2 x 2 x 2 = 16

√100 = 2 x 5 = 10

√256/√100 = 16/10 = 1.6

√2.56 = 1.6

**Example 2 :**

Find the square root of the following decimal number

51.84

**Solution :**

Since we have two numbers after the decimal point, we have to multiply both numerator and denominator by 100.

Here 51.84 can be considered as 51.84/1

√(51.84/1) = √(51.84/1) x (100/100)

= √(5184/100)

Now take separate square roots for both numerator and denominator. = √(5184/100) = √5184/√100 √5184 = √(2x2x2x2x2x2x3x3x3x3) √100 = √(2x2x5x5) |

√1584 = = 2 x 2 x 2 x 3 x 3 = 72

√100 = 2 x 5 = 10

√1584/√100 = 72/10 = 7.2

√15.84 = 7.2

**Example 3 :**

Find the square root of the following decimal number

0.2916

**Solution :**

Since we have four digits after the decimal point, we have to multiply both numerator and denominator by 10000.

Here 0.2916 can be considered as 0.2916/1

√(0.2916/1) = √(0.2916/1) x (10000/10000)

= √(2916/10000)

Now take separate square roots for both numerator and denominator. = √(2916/10000) = √2916/√10000 √2916 = √(2x2x3x3x3x3x3x3) √10000 = √(5x5x5x5x2x2x2x2) |

√2916 = = 2 x 3 x 3 x 3 = 54

√10000 = 5 x 5 x 2 x 2 = 100

√2916/√10000 = 54/100 = 0.54

√0.2916 = 0.54

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

Apart from the stuff given above, if you want to know more about "Square roots of fractions and decimals", 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...

**WORD PROBLEMS**

**HCF and LCM 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**

**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**