Question

(√32-√5)1/3(√32+√5)1/3​

Answer 1

Given: The term (√32-√5)^1/3 x (√32+√5)^1/3​

To find: The product of the above term

Solution:

• So we have provided with the term:

             (√32-√5)^1/3 x (√32+√5)^1/3​

• Now by using the formula: a^m x b^m = (ab)^m

• So applying this formula, we get:

             { (√32-√5) x (√32+√5) }^1/3​

• Now by using the formula: (a - b)(a + b) = a^2 - b^2

• So applying this formula, we get:

            { (√32)²-(√5)² }^1/3​

• Now solving this we get:

            { 32 - 5 }^1/3​

            { 27 }^1/3​

• Now cubic root of 27 is 3, so:

            { 3^3 }^1/3​  = 3

Answer:

          So the product of (√32-√5)^1/3 x (√32+√5)^1/3​  is 3.