Question

5. Find the square root of the following numbers by prime factorisation method.
(a) 25401600
(b) 230400
(c)777924

Answer 1

Answer:

(a) After prime factorization and grouping together prime nos. we get,

$25401600 = {2}^{8} \times {3}^{4} \times 5^{2} \times {7}^{2} \\ or \: 25401600 = {( {2}^{4} )}^{2} \times { ({3}^{2} )}^{2} \times {5 }^{2} \times {7}^{2} \\</p><p>or\sqrt{25401600} = {2}^{4} × {3}^{2} × 5 × 7 = 5040$

Similarly,

(b) $230400 = {({2}^{5 })}^{2} \times {3}^{2} \times {5}^{2} \\ Or, \sqrt{230400} = {2}^{5} × 3 × 5 = 480$

(c) $777924 = {2}^{2} \times {({3}^{2}})^{2} \times {({7}^{2}})^{2} \\ Or, \sqrt{777924} = 2 × {3}^{2} × {7}^{2} = 882$