Simplify radical. Intermediate Algebra
Answer (2)
180 ÷ 2 = 90; 90 ÷ 2 = 45 ; 45 ÷ 3 = 15 ; 15 ÷ 3 = 5 ; 5 ÷ 5 = 1 => 180 = (2^2) * (3^2) * 5 => 180 = 2 ∗ 3 ∗ 5 = 6 5 ;
In the same way we have 245 = 7 5 ; and 320 = 8 5 ;
Finally, 6 5 + 7 5 − 8 5 = 13 5 − 8 5 = 7 5 .
To simplify a radical like 180 , start with its prime factorization, which is 180 = 2 2 × 3 2 × 5 . Then, apply the square root rule to rewrite it as 6 5 . If you combine terms like 6 5 + 7 5 − 8 5 , the final answer is 5 5 .
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