If a=√[8]6-√[8]5, b=√[8]6+√[8]5, c=√[6]6+√[6]5, d= √[4]6+√[4]5, and e=√6+√5, then which of the following is a rational number?

Question

If a=√[8]6-√[8]5, b=√[8]6+√[8]5, c=√[6]6+√[6]5, d= √[4]6+√[4]5, and e=√6+√5, then which of the following is a rational number? (A) abcde (B) a b d e (C) a b (D) c d

Tardigrade Admin · Accepted Answer

Given that, a=√[8]6-√[8]5, b=√[8]6+√[8]5 c=√[6]6+√[6]5 d=√[4]6+√[4]5, e=√6+√5 By inspection, we can reject a b, c d. a b=√[4]6+√[4]5 ∴ a b d=√6-√5 text and a b d e=6-5=1 . ∴ abde is a rational number.

Q. If $a = 86 - 85, b = 86 + 85, c = 66 + 65, d =$ $46 + 45$ , and $e = 6 + 5$ , then which of the following is a rational number?

abcde

$ab d e$

$ab$

$c d$

Given that, $a = 86 - 85, b = 86 + 85$
$c = 66 + 65$
$d = 46 + 45, e = 6 + 5$
By inspection, we can reject $ab, c d$ .
$ab = 46 + 45$
$∴ ab d = 6 - 5 and ab d e = 6 - 5 = 1.$
$∴$ abde is a rational number.

Q. If a=86​−85​,b=86​+85​,c=66​+65​,d= 46​+45​, and e=6​+5​, then which of the following is a rational number?