Max@Math Revolution wrote:[(5√3+3√5)/(√5+√3)]²=?
A. √6 B. √15 C. 15 D. √24 E. 6
An alternate approach is to BALLPARK.
Every test-taker should know the values of common roots.
√3 ≈ 1.7.
√5 ≈ 2.3.
Thus:
[(5√3+3√5)/(√5+√3)]²
≈ [[(5)(1.7) + (3)(2.3)]/(2.3 + 1.7)]²
≈ [(8.5 + 7)]/4]²
≈ (16/4)²
= 4²
= 16.
Only
C is close to 16.
The correct answer is
C.
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