The product \(\sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32}\) equals
a. √2
b. 2
c. \(\sqrt[12]{2}\)
d. \(\sqrt[12]{32}\)

Solution:

Given

\(\sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32}\)

It can be written as

= (2)^1/3 . (2)^1/4 . (32)^1/12

= (2)^1/3 . (2)^1/4 . (2⁵)^1/12

By further simplification

= (2)^1/3 . (2)^1/4 . 2^5/12

We know that a^m × aⁿ = a^{m + n}

= 2^{1/3 + 1/4 + 5/12}

Taking LCM

= 2^{(4 + 3 + 5)/12}

= 2^12/12

So we get

= 2¹

= 2

Therefore, the product is 2.

✦ Try This: The product \(\sqrt[4]{3}.\sqrt[3]{3}.\sqrt[10]{243}\) equals

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

NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 18

The product \(\sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32}\) equals a. √2, b. 2, c. \(\sqrt[12]{2}\), d. \(\sqrt[12]{32}\)

Summary:

The product of two rational numbers can always be written as a rational number. The product equals 2

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