\(\sqrt[4]{\sqrt[3]{2^{2}}}\) equals
a. 2^-1/6
b. 2^-6
c. 2^1/6
d. 2⁶

Solution:

Given

\(\sqrt[4]{\sqrt[3]{2^{2}}}\)

It can be written as

= [(2²)^1/3]^1/4

We know that [a^m]ⁿ = a^mn

= (2²)^1/12

Similarly

= 2^{2 × 1/12}

= 2^1/6

Therefore, equals 2^1/6.

✦ Try This: \(\sqrt[5]{\sqrt[4]{3^{3}}}\) equals

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 17

\(\sqrt[4]{\sqrt[3]{2^{2}}}\) equals a. 2^-1/6, b. 2^-6, c. 2^1/6, d. 2⁶

Summary:

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). So it is equal to 2^1/6

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