# Fill in the blanks:

Question:

Fill in the blanks:

(i) $\sqrt[3]{125 \times 27}=3 \times \ldots$

(ii) $\sqrt[3]{8 \times \ldots}=8$

(iii) $\sqrt[3]{1728}=4 \times \ldots$

(iv) $\sqrt[3]{480}=\sqrt[3]{3} \times 2 \times \sqrt[3]{\ldots}$

(v) $\sqrt[3]{\cdots}=\sqrt[3]{7} \times \sqrt[3]{8}$

(vi) $\sqrt[3]{\cdots}=\sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}$

(vii) $\sqrt[3]{\frac{27}{125}}=\frac{\ldots}{5}$

(viii) $\sqrt[3]{\frac{729}{1331}}=\frac{9}{\ldots}$

(ix) $\sqrt[3]{\frac{512}{\ldots}}=\frac{8}{13}$

Solution:

(i) 5

$\sqrt[3]{125 \times 27}=3 \times \underline{\mathbf{5}}$

$\because \sqrt[3]{125 \times 27}=\sqrt[3]{125} \times \sqrt[3]{27}=\sqrt[3]{5 \times 5 \times 5} \times \sqrt[3]{3 \times 3 \times 3}$

$=5 \times 3$

$=3 \times 5 \quad$ (Commutative law)

(ii) $8 \times 8=64$

$\because \sqrt[3]{8 \times \underline{8 \times 8}}=8$

(iii) 3

$\because \sqrt[3]{1728}=12=4 \times 3$

(iv) 20

$\because \sqrt[3]{480}=\sqrt[3]{\{2 \times 2 \times 2\} \times 2 \times 2 \times 3 \times 5}=2 \times \sqrt[3]{3} \times \sqrt[3]{5 \times 2 \times 2}=\sqrt[3]{3} \times 2 \times \sqrt[3]{20}$

(v) $7 \times 8=56$

$\because \sqrt[3]{7 \times 8}=\sqrt[3]{7} \times \sqrt[3]{8}$

(vi) $4 \times 5 \times 6=120$

$\because \sqrt[3]{4 \times 5 \times 6}=\sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}$

(vii) 3

$\because \sqrt[3]{\frac{27}{125}}=\frac{\sqrt[3]{27}}{\sqrt[3]{125}}=\frac{3}{5}$

(viii) 11

$\because \sqrt[3]{\frac{729}{1331}}=\frac{\sqrt[3]{729}}{\sqrt[3]{1331}}=\frac{9}{11}$

(ix) $13 \times 13 \times 13=2197$

$\because \sqrt[3]{\frac{512}{13^{3}}}=\frac{\sqrt[3]{8^{3}}}{\sqrt[3]{13^{3}}}=\frac{8}{13}$