Question

Find the cube root of each of the following natural numbers:

(i) 1157625 (ii) 250047

Question 27
Find the cube root of : 0.001728

Answer 1

Answer:

(ii) 250047

Step-by-step explanation:

please make as thanks

Answer 2

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given-Numbers:-}}}}}}$

➾(i) 1157625

➾ (ii) 250047

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$\large\underline{\underline{\maltese{\gray{\pmb{\sf{\:To \: Find :-}}}}}}$

➾ The cube root of given natural numbers:

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$\large\underline{\underline{\maltese{\purple{\pmb{\sf{\: Solution-1 :-}}}}}}$

❒ Method Used :

• ➢ By using Prime factorization method

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{i) \sqrt[3]{1157625} }}}}}$

$\qquad{:\implies\sf{{ \sqrt[3]{3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7 } }}}$

$\qquad{\pink\longrightarrow{\blue{\underline{\sf{\sqrt[3]{( {3}^{3} \times {5}^{3} \times {7}^{3} } }}}}}$

$\large\qquad{\qquad{\orange{:\longmapsto{\underline{\boxed{\sf{3 \times 5 \times 7}}}}}}{\pink{\bigstar}}}$

$\large\qquad{\qquad{\orange{:\longmapsto{\underline{\boxed{\sf{105}}}}}}{\pink{\bigstar}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore

➳Cube root of 1157625 is 105

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$\large\underline{\underline{\maltese{\purple{\pmb{\sf{\: Solution-2:-}}}}}}$

• ➢ By using Prime factorization method

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ii) \sqrt[3]{250047} }}}}}$

$\qquad{:\implies\sf{{ \sqrt[3]{3 \times 3 \times 3 \times 3\times 3 \times 3 \times 7 \times 7 \times 7 } }}}$

$\qquad{\pink\longrightarrow{\blue{\underline{\sf{\sqrt[3]{( {3}^{3} \times {3}^{3} \times {7}^{3} } }}}}}$

$\large\qquad{\qquad{\orange{:\longmapsto{\underline{\boxed{\sf{3 \times 3 \times 7}}}}}}{\pink{\bigstar}}}$

$\large\qquad{\qquad{\orange{:\longmapsto{\underline{\boxed{\sf{63}}}}}}{\pink{\bigstar}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore

➳ Cube root of 250047 is 63

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${\green{\underline{▬▬▬▬▬}}{\pink{\underline{▬▬▬▬▬}}{\orange{\underline{▬▬▬▬▬}}{\purple{\underline{▬▬▬▬▬▬}}}}}}$

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$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given-Numbers:-}}}}}}$

➾0.001728

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$\large\underline{\underline{\maltese{\gray{\pmb{\sf{\:To \: Find :-}}}}}}$

➾ To find cube root of 0.001728

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$\large\underline{\underline{\maltese{\purple{\pmb{\sf{\: Solution-3 :-}}}}}}$

➳Let x = 0.001728

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{x = \frac{1728}{1000000} }}}}}$

➳ Now cube root of x is

$\qquad{:\implies\sf{{{ \sqrt[3]{x} = \sqrt[3]{ \frac{1728}{ {10}^{6} } } } }}}$

$\qquad{\pink\longrightarrow{\blue{\underline{\sf{ {\frac{12}{ {10}^{2} } } }}}}}$

$\large\qquad{\qquad{\orange{:\longmapsto{\underline{\boxed{\sf{0.12}}}}}}{\pink{\bigstar}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore

Cube root of 0.001728 is 0.12

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