(i) For n ∈ N, n even, and b > 0, there is a unique a > 0 such that an = b.

(ii) For n ∈ N, n odd, b ∈ R, there is a unique a ∈ R such that an = b. In both cases a is called the nth root of b or radical and is denoted by b1/n or n√b

(i) If n = 2, then nth root is called the square root; if n = 3, then it is called cube root.

(ii) Observe that the equation  x2 = a2, has two solutions x = a, x = −a; but a2 = |a|.

(iii) Properties of exponents given above are still valid for radicals provided each of the individual terms are defined.

(iv) Note that for n ∈ N and a ≠  0 we have

(an)1/n  =  |a| if n is even, a if n is odd

Questions

(1) Simplify

(i)  (125)2/3                Solution

(ii)   (16)-3/4         Solution

(iii)  (-1000)-2/3     Solution

(iv)  (3-6)1/3             Solution

(v)   27-2/3/27-1/3      Solution

(2)  Evaluate (((256)-1/2)-1/4)3           Solution

(3)  Evaluate If (x1/2 + x−1/2)2 = 9/2, then find the value of (x1/2 − x−1/2) for x > 1.        Solution

(4)  Simplify and hence find the value of n: 32n923−n/33n = 27.         Solution

(5)  Find the radius of the spherical tank whose volume is 32π/3 units.      Solution

(6)  Simplify by rationalising the denominator.

(7 + √6) / (3 - √2)         Solution

(7)  Simplify

Solution

(8)  Simplify

If x = √2 + √3 find (x2 + 1)/(x2 − 2)    Solution

Kindly mail your feedback to v4formath@gmail.com

Recent Articles

1. SAT Math Resources (Videos, Concepts, Worksheets and More)

Sep 16, 24 11:07 AM

SAT Math Resources (Videos, Concepts, Worksheets and More)

2. Digital SAT Math Problems and Solutions (Part - 42)

Sep 16, 24 09:42 AM

Digital SAT Math Problems and Solutions (Part - 42)