Question:

Find the cube root of each of the following numbers by prime factorisation method. 

(i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 

(vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125.

Updated On: Dec 1, 2023
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Solution and Explanation

(i) 64

\(\sqrt{64}=\sqrt{2×2×2×2×2×2}\)

\(\sqrt{64}=2×2=4\)

(ii) 512

\(\sqrt{512}=\sqrt{2×2×2×2×2×2×2×2×2}\)

\(=2×2×2=8\)

(iii) 10648

\(\sqrt{10648}=\sqrt{2×2×2×11×11×11}\)

\(=2×11=22\)

(iv) 27000

\(\sqrt{27000}=\sqrt{2×2×2×3×3×3×5×5×5}\)

\(=2×3×5=30\)

(v) 15625 

\(\sqrt{15625}=\sqrt{5×5×5×5×5×5}\)

\(=5×5=25\)

(vi) 13824

\(\sqrt{13824}=\sqrt{2×2×2×2×2×2×2×2×2×3×3×3}\)

\(=2×2×2×3=24\)

 (vii) 110592

\(\sqrt{110592}=\sqrt{2×2×2×2×2×2×2×2×2×2×2×2×3×3×3}\)

\(=2×2×2×2×3=48\)

(viii) 46656

\(\sqrt{46656}=\sqrt{2×2×2×2×2×2×3×3×3×3×3×3}\)

\(=2×2×3×3=36\)

(ix) 175616

\(\sqrt{175616}=\sqrt{2×2×2×2×2×2×2×2×2×7×7×7}\)

\(=2×2×2×7=56\)

(x) 91125

\(\sqrt{91125}=\sqrt{3×3×3×3×3×3×5×5×5}\)

\(=3×3×5=45\)

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