Question

cube root a + 1 x fourth root 5 is mixed surd then the least possible positive integral value of a is​

Answer 1

Given:

Cube root a + 1 x fourth root 5 is mixed surd

To Find:

The least possible positive integral value of a for the above condition to satisfy.

Solution:

A pure surd is said to be a number under a radical sign.

Eg : √4 , √5 .

A mixed surd is said to have a rational coefficient ( ≠ 1 ) to the number under radical sign.

Here the number is ∛(a+1) x $5^{1/4}$ .

• $5^{1/4}$ is already under radical sign.
• So inorder for the product to be a mixed surd,
• ∛(a+1) should be a whole number.
• a + 1 should be the cube of a whole number.
• First cube number = 1³ = 1
• Then a = 0

Given a should positive interger.

• Second least cube = 2³ =8
• a + 1 = 8
• a = 7

Therefore, least positive integral value of a is 7.