# Making use of the cube root table, find the cube root 34.2 . - Mathematics

Sum

Making use of the cube root table, find the cube root
34.2 .

#### Solution

The number 34.2 could be written as $\frac{342}{10}$

Now

$\sqrt[3]{34 . 2} = \sqrt[3]{\frac{342}{10}} = \frac{\sqrt[3]{342}}{\sqrt[3]{10}}$

Also

$340 < 342 < 350 \Rightarrow \sqrt[3]{340} < \sqrt[3]{342} < \sqrt[3]{350}$

From the cube root table, we have:  $\sqrt[3]{340} = 6 . 980 and \sqrt[3]{350} = 7 . 047$

For the difference (350 - 340), i.e., 10, the difference in values

$= 7 . 047 - 6 . 980 = 0 . 067$ .

∴  For the difference (342 -340), i.e., 2, the difference in values

$= \frac{0 . 067}{10} \times 2 = 0 . 013$   (upto three decimal places)

∴ $\sqrt[3]{342} = 6 . 980 + 0 . 0134 = 6 . 993$  (upto three decimal places)
From the cube root table, we also have: $\sqrt[3]{10} = 2 . 154$
∴ $\sqrt[3]{34 . 2} = \frac{\sqrt[3]{342}}{\sqrt[3]{10}} = \frac{6 . 993}{2 . 154} = 3 . 246$

Thus, the required cube root is 3.246.

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.5 | Q 22 | Page 36