## Definition of radical:

A symbol used to indicate square of any number is called radical. The number which is under the root is called radicand.

√3 is called square root of 3.

Example 1:

Simplify 72 to the simplest form

To reduce this number to the simplest form we need to split this number as much as possible.

√72 = √(2 x 2 x 2 x 3 x 3)

If any two numbers which are in the root we can take one of them out of the root.

Here we have 2 and 3 twice. So we can take one from the root.

= 2 x 3 √2

= 6 √2

Now we are going to see more examples

Question 1:

Simplify √ 27 + √ 75 + √ 125 - √ 12

Solution:

= √(3 x 3 x 3) + √(5 x 5 x 3) + √(5 x 5 x 5) - √(2 x 2 x 3)

= 3 √3 + 5 √3 + 5 √5 - 2 √3

= 3 √3 + 5 √3 - 2 √3 + 5 √5

= 8 √3 - 2 √3 + 5 √5

= 6 √3 + 5 √5

Question 2:

Simplify √45 + √80 + √75

Solution:

= √(3 x 3 x 5) + √(2 x 2 x 2 x 5) + √(5 x 5 x 3)

= 3 √5 + 2 √(2 x 5) + 5 √3

= 3 √5 + 2 √10 + 5 √3

Question 3:

Simplify √108 + √200 + √128 - √42

Solution:

= √(2 x 2 x 3 x 3 x 3) + √(2 x 2 x 2 x 5 x 5)

+ √(2 x 2 x 2 x 2 x 2 x 2 x 2) - √(2 x 2 x 2 x 5)

= 2 x 3 √3 + 2 x 5 √2 + 2 x 2 x 2 √2 - 2 √(2 x 5)

= 6 √3 + 10 √2 + 8 √2 - 2√10

= 6 √3 + 18 √2 - 2 √10

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