# Radical expressionsRules for simplifying radical expression. Discuss and give example

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The radical numbers ar numbers written into the form of sqrt(a).

There are rules for simplifying.

Rule (1):

sqrt(a*b) = sqrt(a)* sqrt(b)

sqrt(a/b) = sqrt(a)/sqrt(b)

Example:

sqrt15 = sqrt(3*5) = sqrt3 * sqrt5

sqrt(9/4) = sqrt9/sqrt4 = 3/2

Rule (2):

sqrt(a+-b) does **NOT** equal sqrt(a) +- sqrt(b)

Example:

sqrt(16) = sqrt(8+8) = 4

However, sqrt8 + sqrt8 = 2sqrt2 + 2sqrt2 = 4sqrt2

Then sqrt(8+8) does not equal sqrt8 + sqrt8.

A radical expression is an expression containing a square root. here i have simplify radical expression which is mentioned below:

Evaluate the radical expression when

a= 2 andb= 4.Choices:

A. 9

B. 8

C. 7

D. 6Correct Answer:DSolution:

Step 1: [Substitute the values ofaandbin the given radical expression.]

Step 2: [Find the positive square root.]

Step 3: [Multiply.]

Step 4: [Add.]

Step 5: = 6 [Simplify.]

One rule is to re-write 2 numbers, that are multiplied under the radical sign, under 2 different square root signs.

For instance:

sqrt[(16)*(25)] = sqrt(16)*sqrt(25)

sqrt(400) = 4*5

20 = 20

Another rule states that 2 radical expressions are multiplied, we can re-write the product of radicands under the same radical sign.

For instance:

sqrt(3)*sqrt(4) = sqrt[(3)*(4)]

sqrt(3)*sqrt(4) = sqrt12