Simplify (25–√+37–√)2 . Show your work. Justify each step.
(25–√+37–√)2
= (5–√+6–√)2 [Simplify 25 to 5√ and 37 to 6√]
= (11–2√)2 [Combine like terms]
= 112 – 2(11)(2√) + (2√)2 [Use the formula (a-b)2 = a2 - 2ab + b2]
= 121 - 44√ + 4 [Simplify]
= 125 - 44√ [Combine like terms]
Therefore, the simplified expression is 125 - 44√.
Simplify 4√6/√30 by rationalizing the denominator. Show your work
To simplify 4√6/√30 by rationalizing the denominator, we need to multiply both the numerator and denominator by √30 to eliminate the square root in the denominator.
(4√6/√30) * (√30/√30)
= 4√6√30 / 30
= 4√(6 * 30) / 30
= 4√180 / 30
= 4√(4 * 45) / 30
= 4√4√45 / 30
= 4 * 2√45 / 30
= 8√45 / 30
Therefore, the simplified expression after rationalizing the denominator is 8√45 / 30. This can be further simplified by dividing both the numerator and denominator by 2 to get:
4√45 / 15