Grade 109 grade maths

Write cube root of3,square root of3,and the fourth root of6 in ascending order?

Sarun Sathis

11 Years agoGrade 10

4 Answers

SHAIK AASIF AHAMED

11 Years ago

Hello student,
Please find the answer to your question below
Given (3)^1/3,(3)^1/2,(6)^1/4
Equalizing powers by multiplying and dividing by 12 we get
=(3)^(12)/(3*12),(3)^12/(2*12),(6)^(12)/(4*12)
=(3⁴)^1/12,(3⁶)^1/12,(6³)^1/12
=(81)^1/12,(729)^1/12,(216)^1/12
As in ascending order 81,216,729
So ascending order is(3)^1/3,(6)^1/4,(3)^1/2

Sourabh Singh

11 Years ago

LHS=cos6A-sin6A= (cos²A)³-(sin²A)³
=(cos²A-sin²A)(cos⁴A+sin⁴A+cos²Asin²A)
[sincea³-b³=(a-b)(a²+b²+ab)]
=cos2A((cos²A+sin²A)²-cos²Asin²A
[sincecos2θ=cos²θ-sin²θ]
=cos2A.(1-1/4(2sinAcosA)²=cos2A.(1-1/4.sin²2A )
[sincesin2A=2sinAcosA]
= RHS

Nilanjan Kundu

11 Years ago

First we would take the LCM of the th roots.LCM will be 12. Then we will write cube root of three like (3^4)^1/12, square root of 3 like (3^6)^1/12 and fourth root of 6 like (6^3)^1/12. THis would be

(81)^1/12, (729)^1/12 and (216)^1/12. Therefore, this in ascending order would be (81)^1/12

Aryan Vyas

11 Years ago

In such questions,we have to take the LCM of the powers first.In this case the LCM of 3,2 and 4 =12.Then we have to convert the powers to 12 and the no.which is used for this purpose has to be should be raised inside the radical,i.e.

4×3 root 3⁴ ,6×2 root 3⁶ , 3×4 root 6³

=12 root 81, =12 root 729, =12 root 216

Now it becomes easier to rearrange as the power of the radicals are same.

Now,rearrange as we do for normal nos.

=>12 root 81

=Cube root 3