Radicals and Exponents

The opposite operation to the exponent is known as radical. A radical is an expression which contains the square roots, cube roots etc. For example the expression √49 can also be called as square root of 49 or root of 49. Radicals have the same property of the numbers. The simplification is to reduce the numbers and reduce the power of variables inside the roots.

Exponent of a number shows you how many times the number is to be used in a multiplication.  It is shown as a small number to the right and above the base number.  In this example: 22 = 2 × 2 = 4 ( Another name for exponent is index or power ).

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Examples for Radicals:

Example 1 for radical problem:

Simplify the radical:    √ (144) / (√36)

Step 1: Factors of 144 = 12 × 12

√ (144) = √ (12 × 12)

= √122

Step 2: Square root of 122 = 12

Step 3: Factors of 36 = 6 × 6

√ (36) = √ (6 × 6) = √62

Step 4:  √62 = 6

Step 5: so, √ (144) / √36) = 12 / 6

The answer of the given radical is 12 / 6
Example 2 for radical problem:

Simplify the radical:    3√8 × √12

Step 1: Find the factor of 8 = 2 × 2 × 2

Step 2: Take cubic root of 8 = 2

Step 3: Find the factor for 12 = 2 × 2 × 3

Step 4: Take square root of 12 = 2 √3

Step 5: so, 3√8 × √12 = 2 × 2 √3

The answer for the given radical is = 4√3

Examples for exponents:

EXAMPLE-1:

453 . 454 = 453+4 = 457

EXAMPLE-2:

148 / 145  = 14 8-5 = 143

EXAMPLE-3:

( 92 )3  = 9 2x3  = 96

EXAMPLE-4:

( 11 / 13 )2  = 112 / 122

Algebra is widely used in day to day activities watch out for my forthcoming posts on Triple Integral Spherical Coordinates and Calculus Integration by Parts. I am sure they will be helpful.

EXAMPLE-5:

70 = 1

EXAMPLE-6:

5-3 = 1/ 53