Math Is Fun Forum

lucinda01

Member

Registered: 2008-05-29

Posts: 3

simplifying

when a question asks:  simplify the following

1. a) √12

b) √112

is the answer simply the square root of these numbers?

then

2. express the following in the form (a√c) / b , where a b and c are all integrers

a) (3√11) / (2√3)

b) (5√6) / √7

how do i go about doing this?

appreciate the help, thankyou

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: simplifying

1. wants you to write the square root as a multiple of a smaller square root, in each case.

For example, √12 = √4 x √3 = 2√3.
The method for the other one is similar.

For 2, you need to rationalise the denominator (ie. get rid of any surds in it).
In both of those questions, you just need to multiply the numerator and denominator by the appropriate surd.

So:

Again, you do the other question in a similar way.

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Why did the vector cross the road?
It wanted to be normal.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,341

Re: simplifying

1 (a) √12 = √(4x3) = 2√3

(b) √112 = √(16x7) = 4√7

2. (a) (3√11) / (2√3) = √(33)/2

(b) (5√6)/(√7) = 5√(42)/7.

These processes involve rationalising the denominator in order to have an integral value in the denominator.

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