Find the cube root of 2 63 × 3 66 × 7 69

Given, 2 63 × 3 66 × 7 69 2 63 × 3 66 × 7 69 = 2 63 1 3 × 3 66 1 3 × 7 69 1 3 Use the law of exponent, a m n = a m n , we get, 2 63 1 3 × 3 66 1 3 × 7 69 1 3 = 2 63 3 × 3 66 3 × 7 69 3 = 2 21 × 3 22 × 7 23 Hence, the required cube root is equal to 2 21 × 3 22 × 7 23 .

Find the cube root of 512 ÷ 1331

Given, 512 ÷ 1331 , 512 ÷ 1331 = 512 1331 Prime factorisation of 512 1331 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 11 × 11 × 11 . So, cube root of given number is, 512 1331 3 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 11 × 11 × 11 3 = 2 × 2 × 2 11 = 8 11 Hence, the required answer is 8 11 .

Find the value of: 10 . 24

Given, 10 . 24 We know that for finding the square root of a perfect square n , we have to find the prime factors of n . Then, we need to pair the factors. Now, chose one prime factor from each pair and multiply. Here, we are given to compute the square root of 10 . 24 . First convert the decimal number into fraction, 10 . 24 = 1024 100 Prime factors of 1024 100 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 2 × 2 × 5 × 5 . After choosing one prime from each pair, we get, 1024 100 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 2 × 2 × 5 × 5 = 2 × 2 × 2 × 2 × 2 2 × 5 = 32 10 = 3 . 2 Hence, the value of 10 . 24 is 3 . 2 .

Find the value of: 0 . 1225

Given, 0 . 1225 We know that for finding the square root of a perfect square n , we have to find the prime factors of n . Then, we need to pair the factors. Now, chose one prime factor from each pair and multiply. Here, we are given to compute the square root of 0 . 1225 . First convert the decimal number into fraction, 0 . 1225 = 1225 10000 Prime factors of 1225 10000 = 5 × 5 × 7 × 7 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 . After choosing one prime from each pair, we get, 1225 10000 = 5 × 5 × 7 × 7 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 = 5 × 7 2 × 2 × 5 × 5 = 35 100 = 0 . 35 Hence, the value of 0 . 1225 is 0 . 35 .

Find the value of: 1 . 728 3

Given, 1 . 728 3 , 1 . 728 3 = 1728 1000 3 Prime factorisation of 1728 1000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 2 × 2 × 2 × 5 × 5 × 5 . So, cube root of given number is, 1728 1000 3 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 2 × 2 × 2 × 5 × 5 × 5 3 = 2 × 2 × 3 2 × 5 = 12 10 12 10 = 1 . 2 Hence, the required answer is 1 . 2 .

Find the value of: 0 . 729 3

Given, 0 . 729 3 , 0 . 729 3 = 729 1000 3 Prime factorisation of 729 1000 = 3 × 3 × 3 × 3 × 3 × 3 2 × 2 × 2 × 5 × 5 × 5 . So, cube root of given number is, 729 1000 3 = 3 × 3 × 3 × 3 × 3 × 3 2 × 2 × 2 × 5 × 5 × 5 3 = 3 × 3 2 × 5 = 9 10 9 10 = 0 . 9 Hence, the required answer is 0 . 9 .