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 square root symbol " √ " and the number or expression inside the square root symbol is called the radicand.

Operations with square roots :

Addition, subtraction, multiplication and division of root terms can be performed by some laws. Let us see the rules one by one.

Rule 1 :

Whenever we have two or more root terms which are multiplied with same index, then we can put only one radical and multiply the terms inside the root terms. Rule 2 :

Whenever we have two or more root terms which are dividing with same index, then we can put only one root  and divide the terms inside the root sign. Rule 3 :

nth root of a can be written as a to the power 1/n. Whenever we have power to the power, we can multiply both powers. ## Addition and subtraction of square roots

Addition and subtraction of two or more root terms can be performed with like radicands only. Like radicand means a number inside root sign must be same but the number outside the root sign  may be different.

For example, 5√2 and 3√2 are like terms. Here the numbers inside the roots are same.

If we want to add, subtract, multiply or divide two or more root terms, the order must be same.

If the order of the radical terms are not equal, then we have to convert them with same order and we can perform multiplication or division.

Let us see some examples based on the above concepts.

Example 1 :

Simplify the following

4√3, 18√2, -3√3, 15√2

Solution :

=  4√3 + 18√2 - 3√3 + 15√2

To simplify the above terms, we need to combine the like terms

=  4√3  - 3√3 + 18√2 + 15√2

=  (4 - 3) √3 + (18 + 15) √2

=  1√3 + 33√2

=  √3 + 33√2

Example 2 :

Simplify the following

2∛2, 24∛2, - 4∛2

Solution :

=  2∛2 + 24∛2 - 4∛2

=  (2 + 24 - 4) ∛2

=  22 ∛2

Example 3 :

Multiply ∛13 x ∛5

Solution :

=  ∛13 x ∛5

Since the index of both root terms are same, we can write only one root sign and multiply the numbers.

=  ∛(13 x 5)

=  ∛65

Example 4 :

Multiply 15√54 ÷ 3√6

Solution :

=  15√54 ÷ 3√6

Since the index of both root terms are same, we can write only one root and divide the numbers.

=  (15/3)√(54/6)

5√9  ==>  5√(3 x 3)  ==> 5 x 3  ==> 15

Example 5 :

Multiply (48)1/4 ÷ (72)1/8

Solution :

=  (48)1/4 ÷ (72)1/8

Since the index of the above  root terms are not same, we need to convert the power 1/4 as 1/8.

=  (48)(1/4) x (2/2) ÷ (72)1/8

=  (48)(2/8) ÷ (72)1/8

=  482 (1/8) ÷ (72)1/8

=  [(48 x 48) ÷ (72)]1/8

=  [2304 ÷ 72]1/8

=  (32)1/8

## Related topics Apart from the stuff "Perpendiculars and bisectors" given in this section, 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

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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 