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Cube Root Using Prime Factorisation

√125 × 64 = ?...

Question

$\sqrt[3]{125 \times 64}$ = ?
(a) 100 (b) 40
(c) 20 (d) 30

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Solution

$\sqrt[3]{125 \times 64} = \sqrt[3]{5 \times 5 \times 5 \times 4 \times 4 \times 4} = \sqrt[3]{5^{3} \times 4^{3}} = 5 \times 4 = 20$

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\sqrt[3]{125 \times 64} = ?

(a) 100
(b) 40
(c) 20
(d) 30

Q. Mark whether true or false.
(a) 36 + 64 = 64 + 36 _____
(b) 125 × 8 = 8 × 125 _____
(c) 683 × 1 = 1 × 683 _____
(d) 100 ÷ 5 = 5 ÷ 100 _____
(e) 36 ÷ 4 = 4 ÷ 36 _____

\sqrt[3]{125 \times 64} = \sqrt[3]{125} \times \sqrt[3]{64}

125 a^{3} + b^{3} + 64 c^{3} - 60 a b c

Q. Factorize:
125a³ + b³ + 64c³ − 60abc

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