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.
(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
\(\sqrt{91125}=\sqrt{3×3×3×3×3×3×5×5×5}\)
\(=3×3×5=45\)
State true or false.
(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeros.
(iii) If square of a number ends with 5, then its cube ends with 25.
(iv) There is no perfect cube which ends with 8.
(v) The cube of a two digit number may be a three digit number.
(vi) The cube of a two digit number may have seven or more digits.
(vii) The cube of a single digit number may be a single digit number
Fill in the blanks using the correct form of the verbs in brackets.
My little sister is very naughty. When she ____ (come) back from school yesterday, she had _____(tear) her dress. We _____(ask) her how it had _____(happen). She ______(say) she _____ _____ (have, quarrel) with a boy. She _____ _____ (have, beat) him in a race and he _____ ____ (have, try) to push her. She _____ ____ (have, tell) the teacher and so he _____ _____ (have, chase) her, and she _____ _____ (have, fall) down and _____ _____ (have, tear) her dress.