Question

FIND the cube root of 4741632 by estimation method only otherwise I will report​

Answer 1

$\boxed{\red{\underline{ \bf \huge ANSWER </p><p> }}}$

$\bf \implies \: \sqrt[3]{4741632} = 168$

$\boxed{\green{\underline{ \bf \: GIVEN </p><p> }}}$

$\bf \implies 4741632$

$\boxed{\orange{\underline{ \bf \: TO \: \: FIND </p><p> }}}$

$\implies \bf \: the \: cube \: root \: of \: 4741632 \:$

$\boxed{\blue{\underline{ \bf \huge SOLUTION </p><p> }}}$

$\bf \implies \qquad \sqrt[3]{4741632} \\ \\ = \quad \underbrace{ \sf 4741} _{ \mathtt{ II}} \underbrace{632} _{ \mathtt{I}} \\ \\ \\ \mathtt I = \sf 63 \underline{2} \\ \\ \therefore \sf \quad {8}^{3} = 51 \underline{2} \\ \\ \therefore \sf \quad unit \: place = 8 \\ \\ \qquad \mathtt{II} = \sf 474 \underline{1} \\ \\ \therefore \quad \sf 4096 < 4741 < 4913 \\ \\ \therefore \sf \quad {(16)}^{3} < 4741 < {(17)}^{3} \\ \\ \qquad \sf \because 16 \: is \: smaller \: than \: 17 \\ \\ \qquad \Rightarrow \bf \quad \sqrt[3]{4741632} = 168$

$\bf \: Hence \: \: the \: \: cube \: \: root \: \: of \: 4741632 \: \: is \: \: 168$

$\boxed{\green{\underline{ \bf \: ADDITIONAL INFORMATION </p><p> }}}$

$\boxed{\begin{minipage}{10 cm} \\ \underline{ \underline{ \bf{some \: notes \: : }}} \\ \\ \tt (i) \: Square of an even number is always even \\ \\ \tt Example : ( 8 )^2 = \tt{ 64 \: ( even )} \\ \\ \tt (ii) \: Squares \: \: of \: \: odd \: \: numbers \: \: are \: \: always \: \: odd \: \: \\ \\ \tt Example : ( 7 )^2 = \tt{ 49 \: ( odd )} \\ \\ \tt (iii) \: \: one \: \: number \: \: ending \: \: with \: \: 2,3,7, 8 \: \: are \: \: not \: \: perfect \: \: squares \\ \\ \tt Example : =32,243 \: ( \: not \: a \: perfect \: square \: ) \end{minipage}}$

Answer 2

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Given :-

✴ The number 4741632.

To Find :-

▶It's Cube root

Answer :-

√4741632 = 168 × 168 × 168 = (168)³

Calculation :-

According to the question ,

Method :- ▶ Estimation ◀

Deviding in 2 parts,

• First part 632

• Second part=4741

As, 16³ <4741<17³

We, will write smallest number = 16

➡ And rest 632 we know that it last digit is 2 and

8³-512 it last digit is also 2.

↗Therefore we will write 168,

✏ 168³ =4741632

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