Subscribe to our βΆοΈYouTube channelπ΄ for the latest videos, updates, and tips.
Home | About Us | Contact Us | Privacy | Math Blog
In division of surds we need to divide a given surd by another surd the quotient is first expressed as a fraction. Then by rationalizing the denominator the required quotient is obtained with a rational denominator. For this the numerator and the denominator are multiplied by appropriate rationalizing factor. In rationalization of surds the multiplying surd-factor is called the rationalizing factor of the given surd.
Division of surds in general can be obtained by following the law of indices.
aβxΓ·bβx= aβxbβx= x(1aβ1b).
From the above equation we can understand that if surds of rational number x are in different orders, then the indices are expressed in fraction and division is obtained by the subtraction of indices of the surds. Here surds of rational number x are in order a and b, so the indices of the surds are 1a and 1b and after division the result index of x is (1aβ1b).
If the surds are in same order, then division of surds can be done by following rule.
aβxΓ·aβy= aβxaβy= aβxy.
From the above equation we can understand that if two or more rational numbers like x and y are in a same order a, then division of those surds can be obtained by division of the radicands or rational numbers of the surds.
In division if the surds are not in same order, we can convert them in same order to obtain the result of a division problem. But first we should try to express the surds in simplest forms and compare with other surds that they are similar surds or equiradical or dissimilar. Whatever the surds are, we can multiply the rational coefficients.
Sometimes for division of surds, we need to rationalize the denominator to get a simpler form and obtain a result. For this both numerator and denominator need to be multiplied by appropriate rationalizing factor.
Like for example 2βx2βy
= 2βxΓ2βy2βyΓ2βy
=2βxyy
In the above example 2βy is the denominator and rationalizing factor for 2βy is 2βy. So 2βy is multiplied to both the nominator and denominator to rationalize the surd.
Now we will solve some problems to understand more on division of surds:
1. Find the division of 2β12 by 2β3.
Solution:
2β12 Γ· 2β3
= 2β123
= 2β4Γ33
= 2β4
= 2β22
= 2.
2. Divide: βx by βy
Solution:
βx by βy
= βx Γ· βy
= βx/βy
= βxy
3. Find the division of 2β5 by 2β3.
Solution:
2β5 Γ· 2β3
= 2β52β3
= 2β5Γ2β32β3Γ2β3 β¦.multiplying 2β3 as rationalizing factor
= 2β153.
4. Divide the first surd by the second surd: β32, β8
Solution:
β32 divided by β8
= β32 Γ· β8
= β328
= β4
= 2.
5. Find the division of 2β3 by 2β2β1.
Solution:
2β3 Γ· 2β2β1
= 2β32β2β1
As the denominator is 2β2β1, for the division, we need to multiply it with a rationalizing factor 2β2+1.
= 2β3(2β2+1)(2β2β1)(2β2+1)
= 2β3Γ2β2+2β32β1β¦.. as we know (a+b)(aβb)=a2βb2
= 2β6 + 2β3.
6. Find the quotient dividing the surd β96 by the surd β16.
Solution:
Required quotient
= β96 Γ· β16
= β9616
= β6.
7. Find the division of (xβ1) by 2βxβ1.
Solution:
(xβ1) Γ· 2βxβ1
= (xβ1)2βxβ1
= ((2βx)2β12)2βxβ1
= ((2βx+1)(2βxβ1)2βxβ1β¦.as we know a2βb2=(a+b)(aβb)
= 2βx+1.
8. Divide: β5 by β7
Solution:
β5 divided by β7
= β5 Γ· β7
= β57
= β5Γβ7β7Γβ7, [Rationalization of denominator of surds]
= β35/7.
β Surds
11 and 12 Grade Math
From Division of Surds to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Jul 16, 25 02:45 AM
Jul 16, 25 02:33 AM
Jul 15, 25 11:46 AM
Jul 15, 25 02:01 AM
Jul 14, 25 01:53 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.