Question

Use the prime decomposition of integers to express the listed radical in its minimal expression. Do not use decimals.

Answer 1

Answer:

(A) $210\sqrt{5$

(B) $210\sqrt{14}$

(C) $1980\sqrt{33}$

(D) $37\sqrt{5}$

Step-by-step explanation:

$\sqrt{220500} = \sqrt{2^2*3^2*5^2*7^2*5} = 2*3*5*7\sqrt{5} =210\sqrt{5$

$3\sqrt{68600} = \sqrt{2^2*2*5^2*7^2*7} = 3*2*5*7\sqrt{14} =210\sqrt{14}$

$3\sqrt{3267}\sqrt{4400} = 3\sqrt{3^2*3*11^2}\sqrt{2^2*2^2*5^2~11} = 3*3*11\sqrt{3}*2*2*5\sqrt{11} =1980\sqrt{33}$

$\sqrt{1125} + \sqrt{2420} = \sqrt{3^2*5^2*5} + \sqrt{2^2*11^2*5} = 3*5\sqrt{5} + 2*11\sqrt{5} =15\sqrt{5} + 22\sqrt{5} = 37\sqrt{5}$