# 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} . (2^{5})^{1/12}

By further simplification

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

We know that a^{m} × a^{n} = a^{m + n}

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

Taking __LCM__

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

= 2^{12/12}

So we get

= 2^{1}

= 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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